The champions hit the woodwork twice in quick succession in the first half through Raheem Sterling and Sergio Aguero, but found themselves behind shortly before the hour mark when Willy Boly bundled the ball in - although replays showed that the final touch came off his arm.
City responded with a thumping Aymeric Laporte header to equalise, but they could not find a winner and were denied by the woodwork again in the final minute when Aguero's free kick crashed against the crossbar.
Find out how all of the action unfolded courtesy of Sports Mole's minute-by-minute updates below.
Hosts Wolverhampton Wanderers are yet to pick up their first win back in the big time, and test do not come any bigger than this Manchester City team, who tore Huddersfield apart last week to reassume their place at the top of the Premier League table.
This match pits together two teams who love to play open, attacking football - and achieved great success doing so last season - so hopefully we will be in for a cracker today.
First, though, let's have a look at the team news...
Well, we'll start with the champions (of the Premier League), and the first thing to note is that Pep Guardiola has switched back to a 4-3-3 formation, having played with three at the back during the rout of Huddersfield Town.
Whether that more attacking formation is one Guardiola will only look to deploy at home and against teams he expects to sit back remains to be seen, but for this one he has reverted back to his usual system, rather than sticking and matching Wolves' formation.
The Argentine already has five goals this season including the Community Shield, netting the first hat-trick of the new campaign in the rout of Huddersfield last time out. Guardiola has reportedly claimed that this is the best Aguero he has ever seen during his time at the club, and he is certainly the number one threat Wolves will have to look out for today.
That said, Aguero has failed to score in his last six Premier League away games, since netting in the 4-0 win at Swansea on December 13.
The quality of this Man City team is perhaps best emphasised by the bench they have named today. Stones, Sane, Mahrez, Jesus and Otamendi - the latter of whom was arguably the league's best defender last season - all fail to make the starting lineup, even in the absence of the injured Kevin De Bruyne.
David Silva's superb free kick against Huddersfield leaves him just one goal away from 50 in the Premier League now, but the main goal threat may come from Sterling, who has been directly involved in seven goals in Man City's last seven away games, scoring three and setting up four more.
The hosts name an unchanged team from the one which was beaten by 10-man Leicester last time out, with Nuno keeping faith in his 3-4-3 formation despite a slow start to the campaign in terms of results.
Traore has always been a handful, though, and to make the step up he must now focus on improving his end product. The former Barcelona man has all of the attributes to become one of the most feared wingers in the Premier League, but his delivery is too inconsistent at the moment.
The 21-year-old picked up a brilliant goal and an equally impressive assist on his Premier League debut during the draw with Everton, and he is likely to be key if Wolves are to get anything out of this game today. Perhaps the biggest compliment I can give him is that he wouldn't look out of place playing for the opposition here.
Raul Jimenez will lead the line again up front, having scored on his debut against Everton, with last season's top-scorer Jota playing in a slightly wider role and Costa on the opposite flank.
It is not a tag Wolves are used to under Nuno, though, having cruised to the Championship title last season. Hopes were high of a quick start to life back in the top flight, but while the performances have been encouraging so far, the results have not matched up.
Still, the newly-promoted side have only managed one point from those two games, though, and they had to come from behind twice to get it against Everton - despite having a man advantage for more than half of the match.
Wolves hit the woodwork three times at the King Power Stadium and missed a host of other chances, while the two goals they conceded came via a Doherty own goal and a deflected Maddison strike.
There have certainly been enough signs in those opening two outings to encourage Nuno and the fans, but the Premier League is unforgiving and Wolves will need to learn that sooner rather than later.
They certainly look better equipped to stay up than the last time they were at this level, and many have tipped them for a top-half finish, but first they must get that opening win under their belt.
One encouraging statistic is that the Championship winners have beaten the Premier League champions at home in each of the past two seasons, with Burnley overcoming Leicester in 2016-17 and Newcastle easing past Chelsea last term, but this Man City team is a different kettle of fish altogether.
Nuno's side are unbeaten in their last 10 competitive outings here at Molineux and have lost just once here in the past 12 months. Wolves lost only two games in front of their own fans throughout last season, and the most recent of those came at the hands of Cardiff in January.
Of course, they are a lot better now than they were on their last season in the Premier League, but to end that run against this Man City team today would be some achievement.
Not even the Invincibles or the very best of Sir Alex Ferguson's Manchester United sides rolled into town with most expecting them to score bucketloads of goals wherever they went, and Man City have shown no signs of slowing down after last season's record-breaking feats.
The second statement came last weekend when they hammered Huddersfield 6-1 at the Etihad Stadium - an impressive result at any stage of the season but particularly good with arguably their best player injured and Guardiola still concerned about fitness levels after the World Cup.
David Wagner's side held Man City to a goalless draw at the Etihad and restricted them to fewer shots on target than any other Premier League team over their two games in 2017-18, so for City to simply swat them aside so early in the new campaign is ominous for the other 19 teams.
Victory today would also see City become the first defending champions to win their first three games of the following since season 2011-12, when United started with nine points out of nine - although that term they famously lost the title in the final kick to Aguero and Man City.
Just three games into the campaign and they have easily beaten two top-six rivals without conceding, before recording the biggest win of the campaign so far against a team they had trouble with last term.
It may have been a quiet summer in the transfer window, but City only seem to have improved from last term.
That is easier said than done against a team in such relentless form, though, and they come into this match having won seven and lost none of their last eight Premier League games, including their last four in a row.
Their only defeat in their past 29 Premier League games against newly-promoted teams came at the hands of Burnley in 2015 too, while they are unbeaten in 12 such fixtures under Pep Guardiola.
City arrive at Molineux having won their last seven Premier League away games on the bounce, with their last defeat coming at the hands of Liverpool in January. Indeed, that is their only defeat on the road in their last 23 Premier League away games, stretching back to April 2017.
I have little doubt that Wolves will be fine and pick up regular points this season, and against almost any other team I would back them to get something here at Molineux. However, it is almost impossible to go against Man City in this form, so I will predict an away victory.
SPORTS MOLE SAYS: Wolves 1-3 Man City
Wolves also beat City here in 2010, but those are their only two victories against today's opponents in eight previous Premier League meetings, with five defeats and one draw.
Wolves do have the distinction of being one of only two teams - alongside Wigan - to have prevented City from scoring last term, though.
Man City's most recent visit to this stadium came in April 2012, when Aguero and Nasri were on the scoresheet in a 2-0 victory which took Roberto Mancini's side one step closer to their dramatic title success that year.
WOLVES STARTING XI: Patricio; Bennett, Coady, Boly; Doherty, Moutinho, Neves, Castro; Costa, Jimenez, Jota
MAN CITY STARTING XI: Ederson; Walker, Kompany, Laporte, Mendy; Fernandinho, Gundogan, Silva; Sterling, Bernardo, Aguero
Jota goes for goal himself but sees his effort deflect into the path of Jimenez, who is left with a simple finish from close range. He had just strayed a yard offside from the initial shot, though!
The ball drops to Sterling around 25 yards from goal and he takes a touch before unleashing a brilliant, swerving half-volley towards the top corner. Patricio's save is every bit as impressive, though, as he claws it against the bar with one hand.
Wolves have held their own for the most part against the defending champions, but they were on the back foot for a spell in that first half and will no doubt need to survive plenty more pressure if they are to get anything out of this game.
However, the celebrations were soon cut short by the linesman's flag, and the replays showed that it was a very good decision from the officials. Kompany had given the ball away to spark the attack, but Man City got away with it.
Patricio was beaten for that one, but the Wolves keeper pulled off a stunning save just a minute later to turn Sterling's brilliant half-volley against the crossbar.
Wolves will be pretty pleased with their performance from that opening 45 minutes, but at the risk of stating the obvious, the job is only half done. Keeping Man City at bay for 45 minutes is difficult enough - doing it for 90 minutes is something few teams can manage.
He eventually does get the shot away, but Ederson responds with a fine stop to keep out the powerful effort at his front post.
Moutinho swings a beauty of a ball into the box and one Wolves player gets the faintest touch on it before Boly bundles it into the far corner. It looks like a legitimate - if a little messy - goal in normal time, but the replay shows that the final touch came off the hand of Boly!
Cue the calls for VAR!
Gundogan clips the free kick into a perfect area and Laporte attacks it really well. Patricio has no chance with that one. Brilliant header.
City can point to a lack of luck for sure - they hit the woodwork three times with really good efforts - but Wolves refused to forsake their own attacking style and were impressive for long spells here.
Thank you very much for joining Sports Mole for today's early Premier League kickoff as newly-promoted Wolves hold champions Manchester City to a draw at Molineux! I will leave you with our match report, and be sure to stick around for reaction too.
From me, though, it is goodbye for now!