Ander Herrera and Anthony Martial were also on the scoresheet either side of a Victor Camarasa penalty before half time, and a second-half brace from Jesse Lingard saw United register a five-goal haul for the first time since the days of Sir Alex Ferguson.
Find out how all of the action unfolded courtesy of Sports Mole's minute-by-minute updates below.
Today marks the first game of the post-Mourinho era, with Cardiff City the opposition in South Wales. It is a match the visitors are favourites for, but it is also one that will not be as easy as it might appear on first glance.
We will have a close look at exactly why in a short while, but first let's see who Solskjaer has chosen in his maiden United XI...
Well, we'll have to start with the visitors and the first thing to note is that Paul Pogba returns to the starting lineup, having been forced to watch on as an unused sub during the defeat to Liverpool last weekend.
The World Cup winner may gain more than most from the sacking of Mourinho following the breakdown of their relationship, and as he makes only his fourth league start since October, now is the time for him to really start showing what he can do in the Premier League.
The striker is understood to have been granted compassionate leave by Mourinho prior to his sacking, and he remains unavailable today which means that Marcus Rashford will leave the line for the visitors today.
Martial has enjoyed spurts of good form so far this season but has tailed off a little in recent games, but he is another one of the players who may be relishing a fresh start under a new manager.
Interestingly, there is no Antonio Valencia even on the bench, so his hopes of working his way back into the first-team thinking do not look great at this stage, while Smalling remains sidelined.
There was an outside chance that Bennett might recover in time for this one, but it would have been a risked as he had not trained all week. As it is, the fit-again Greg Cunningham replaces him at left-back.
Warnock did suggest in his per-match press conference that a couple of unnamed players were suffering from "little niggles", but they clearly cannot be too serious given the lack of chopping and changing.
The 24-year-old is Cardiff's top scorer with four league goals this season and will hope to trouble what has been a very leaky United defence this season.
Hoilett will pose a threat on the counter-attack and also scored at Vicarage Road at the weekend, while Murphy on the opposite flank has also been dangerous at times this season.
It is an intriguing first match for Ole Gunnar Solskjaer too, and many of the Cardiff supporters will have raised their eyebrows at the Norwegian being named as Jose Mourinho's temporary successor.
There is another shock elsewhere as Leicester topple Chelsea at Stamford Bridge, so United will be hoping that the trend of surprises does not extend into this evening kickoff.
One thing the appointment should achieve is to get the fans back onside as Solskjaer is a club legend having won 11 trophies in 11 years as a player, before taking charge of their reserve team too.
The writing had been on the wall for some time amid reports of bust-ups with players, disagreements with the board and, most importantly, a string of poor results on the pitch. Mourinho's style of football was also the cause of much frustration, and already it feels like some weight has been lifted off United's shoulders.
Last weekend's embarrassingly one-sided defeat to Liverpool left United sixth in the Premier League table and 19 points off the leaders - a gap that has since grown to 22 points courtesy of Liverpool's win last night.
Even so, to be sitting 11 points off the top four at this stage of the season - and only 14 clear of the relegation zone, incidentally - is a huge disappointment for the club.
Just last season United were 12 points better off at this stage of the campaign, and United come into today's match with just one win from their last six top-flight outings.
United have shipped 29 goals already this term, which is more than 19th-placed Huddersfield after 17 games and also more than they conceded in the whole of last season. The last time they let in more in their opening 17 games of a top-flight campaign was in 1962-63.
Indeed, United have remarkably lost their last three Premier League away games against promoted teams - as many as in their previous 36 such matches prior to that - and could lose four in a row for the first time since 1961.
Whatever the case, Cardiff will conjure up that underdog spirit and will look to continue their superb recent form here in front of their own fans.
Not since January 1961 have Cardiff won four top-flight home games on the bounce - a run which began with a 3-0 triumph over Manchester United, incidentally - while they could also keep back-to-back clean sheets in top-flight home games for the first time since April 1957.
The Bluebirds were the overwhelming favourites to be relegated, bottom of the table and a long way from safety, before the season began. However, now approaching the halfway stage of the campaign, they sit two points clear of the bottom three.
Cardiff are now surprisingly the highest scorers in that mini-league of the bottom seven - or at least they were at the start of the day - but the concern comes at the other end, where only Fulham conceded more in the opening 17 games.
I have already mentioned Cardiff's impressive home form, with 13 of their 14 points coming here in South Wales, but nine of those points have also been won from losing positions, so there is certainly fight in Warnock's side.
This is such a hard one to call as United are something of an unknown quantity under Solskjaer at this stage. Cardiff's home record is hugely impressive, but I have a feeling United's players will play with the shackles off now that Mourinho has gone.
SPORTS MOLE SAYS: Cardiff 1-2 Man Utd
The Bluebirds ran out 3-0 winners on that occasion, but United have gone on to win five of the subsequent seven meetings.
The first - and United's most recent away games against the Bluebirds - came in November 2013 when Cardiff scored a stoppage-time equaliser to pull off a famous 2-2 draw with United, who has scored through Rooney and Evra.
Robin van Persie and Ashley Young scored on that occasion as United eased to a 2-0 win at Old Trafford.
CARDIFF STARTING XI: Etheridge; Ecuele Manga, Morrison, Bamba, Cunningham; Gunnarsson, Arter, Camarasa; Hoilett, Paterson, Murphy
MAN UTD STARTING XI: De Gea; Young, Lindelof, Jones, Shaw; Herrera, Matic, Pogba; Lingard, Rashford, Martial
The keeper may have to look at himself there as it was on his side, but he was nowhere near it.
The middle picks up the ball 25 yards from goal and tries his luck. It is a decent strike, but hits Cunningham and that is what takes it looping beyond the despairing dive of Etheridge and into the top corner.
That should raise the volume levels inside the Cardiff City Stadium!
It is a move full of one-touch confidence as Martial gives it to Pogba, who gives it to Lingard, who gives it back to Martial breaking into the box. From there he only has the keeper to beat, and he slides his finish past the keeper into the bottom corner.
Beautiful football from the visitors.
United have dominated the possession and have played some lovely football at times - the type of which we have not seen from them for a long time - and there is a long way back for Cardiff now.
The United man went the goalkeeper's side, but Etheridge took a step the other way and then got nowhere near the ball. It was a good strike from Rashford, but Etheridge should have saved it.
Having been on the wrong end of a couple of deflections last weekend, this time they benefited from one as Herrera's 25-yard strike hit Cunningham and looped past Etheridge into the top corner.
Rashford had given the spot kick away with a handball when leaning into the ball and trying to chest it down, and despite United's protests the officials had no doubt. United soon restored their two-goal advantage, though, with Martial capping off a lovely move with a smart finish.
Rashford got the new era off to a perfect start with a goal after only three minutes, and further strikes from Herrera and Martial put United in control at the break - despite Camarasa pulling one back for Cardiff at one stage.
Jesse Lingard then made completely sure of the points with a second-half brace to leave United now eight points off the top four and no doubt feeling a lot better about themselves.
Thank you very much for joining Sports Mole for today's match as Manchester United get the post-Jose Mourinho era off to a perfect start with their best performance and biggest scoreline of the season. 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!