Juve hit the woodwork twice and squandered a string of chances before being punished, though, as Juan Mata levelled things up with an 86th-minute free kick and Alex Sandro scored an unfortunate own goal four minutes later.
Find out how an incredible night unfolded courtesy of Sports Mole's minute-by-minute updates below.
These are two of the giants of European football, but there was a noticeable gulf between the two sides at Old Trafford a fortnight ago, despite Juve only winning by a goal to nil. Tonight's hosts are on the brink of qualifying with two games to spare, whereas Man Utd could really do with a shock win in Turin.
Let's start with a look at the team news...
Well, we'll start with the visitors, whose headline news in the buildup to the match was that Romelu Lukaku was not included in the squad due to an injury which could also rule him out of Sunday's Manchester derby.
As expected, Alexis Sanchez leads the line in his absence - as he did against Bournemouth at the weekend - and the Chilean will be making his 50th Champions League appearance tonight.
Ander Herrera also had an impact off the bench at the weekend and he is rewarded with a start tonight, replacing Fred in the midfield trio alongside Matic and Pogba.
The winger has scored five goals in his last four league games for United and was also on the scoresheet during the victory over Young Boys on matchday one, but he barely got a sniff during the reverse fixture at Old Trafford two weeks ago.
Pogba enjoyed four successful years as a Juventus player, scoring 28 goals in 124 Serie A appearances for the club and helping them to win the title in each of his seasons there. The World Cup winner also featured in the 2015 Champions League final for the Old Lady.
Another World Cup winner takes his place to emphasise the strength in depth available to Juventus, though, with Sami Khedira coming into the starting lineup for his first appearance since matchday one.
Benatia and Cancelo are the other two players to drop out, with De Sciglio switching from left-back to right-back for tonight's match. There is also a place on the bench for Mario Mandzukic, who picked up an ankle injury during the buildup to the reverse fixture but has recovered in time to make the matchday squad for this one.
The Argentine scored a hat-trick against Young Boys on matchday two before getting the only goal of the game at Old Trafford last month, so he is one player United will need to keep a very close eye on tonight.
Since then, the five-time Ballon d'Or winner has gone 389 minutes and 15 shots without a goal, although he is still in fine form domestically with seven goals and five assists in his last eight Serie A outings.
Tonight will be a particularly special occasion for him considering his United connections, having spent six years at the club and helped them to the 2008 Champions League title in addition to three Premier League crowns, the FA Cup and two League Cups. In all, Ronaldo scored 118 goals in 292 appearances for United.
The striker's arrival from Real Madrid in the summer was a major coup for Juventus and will surely only help them end their wait for success in this tournament - a drought which stretches back to 1996. Juve have been in five finals since then, but have lost them all.
The Bianconeri have made light work of a group which also includes United and Valencia to sit top of the pile, already five points clear of their closest challengers - although that gap could be cut before kickoff with Valencia currently beating Young Boys 3-1.
A fifth successive year in the last 16 looks inevitable, then, and Juve are also the only team in the entire group stages yet to have conceded a goal. Borussia Dortmund, to their credit, also kept clean sheets in each of their first three group games, but they conceded twice against Atletico Madrid last night to leave Juve as the only unbreached backline.
The following two games have been easier, with Dybala's hat-trick downing Young Boys before they outclassed United at Old Trafford two weeks ago, running out much more comfortable victors than the 1-0 scoreline suggests.
Indeed, the only two matches Juventus have lost in their last 50 outings across all competitions have both come at home too - against Napoli and Real Madrid in April - so perhaps there is a glimmer of hope for United to get a better result here than they managed at Old Trafford.
In terms of group games, Juventus have lost only one of their last 35 in front of their own fans - a run which stretches back to Manchester United's last visit here in February 2003, during the second group stage that season.
Allegri is a man used to winning, too. He has maintained and even improved upon the winning team he took over, taking their run of league titles to an unprecedented seven in a row, and adding the Coppa Italia crown in each of the last four seasons too.
Juve are already six points clear at the top of Serie A this season, but their challenge now is to replicate that domestic form on the European stage.
The Red Devils look likely to kick this game off having dropped down to third in the standings courtesy of Valencia's impending win over 10-man Young Boys, and defeat in Turin would leave them a point behind the Spaniards with only two games remaining - not to mention eight off Juve.
Mourinho will be desperate to avoid that showdown in Spain, but it would be a fairly major shock if they were to get anything out of this game considering how easily they were outclassed in the reverse fixture.
It made for another lacklustre European display from the Red Devils following their goalless draw with Valencia on matchday two, meaning that their solitary victory - and goals - of the group stages so far came in the 3-0 win over Young Boys in their opening match.
Things are at least better at the other end, where Dybala's goal was the first they had conceded in this season's competition. As a result, only Juve themselves have conceded fewer in the group stages, which is in stark contrast to their Premier League defensive record of 18 goals conceded and only one clean sheet.
The Italian champions will be firm favourites to do it again tonight, although United are coming into the match off the back of successive wins for the first time since mid-September.
The Red Devils needed to hang on against Everton last month before bouncing back from a dreadful first-half display against Bournemouth at the weekend to eventually win 2-1 in stoppage time. However, they have still only won three of their last nine games across all competitions.
Mourinho's side have also not conceded more than one goal in any of those 10 matches, although that is under serious threat tonight and it could be quite a humbling week for the Red Devils considering they also face Manchester City away from home in the derby on Sunday.
Juve were so comfortably the better team at Old Trafford that it is difficult to look past them to win again tonight, and with home advantage behind them it should look a lot better on the scoreboard too.
SPORTS MOLE SAYS: Juventus 3-0 Man Utd
The Red Devils' last visit to Turin also produced a result just as impressive as Giggs scored twice and Van Nistelrooy helped himself to another in a 3-0 win for United in February 2003.
Juve edge the all-time record between the two teams, though, having won six to United's five of their previous 14 meetings courtesy of that victory at Old Trafford a fortnight ago.
United, meanwhile, are unbeaten in their last four away games against Italian clubs, although the defeat last month ended what was an eight-game unbeaten streak against Serie A teams home and away.
JUVENTUS STARTING XI: Szczesny; De Sciglio, Chiellini, Bonucci, Alex Sandro; Khedira, Pjanic, Bentancur; Dybala, Cuadrado, Ronaldo
MAN UTD STARTING XI: De Gea; Young, Smalling, Lindelof, Shaw; Herrera, Matic, Pogba; Lingard, Sanchez, Martial
The possession and chances have fallen the way of Juventus, but United have by no means been overrun and are much more competitive in this game than they were at Old Trafford last month.
Khedira was unmarked in the middle but dragged his finish a fraction too much and saw it come off the post on its way behind, with De Gea completely beaten.
However, the Khedira chance is the only really big one that they have created so far, and they are finding things a lot more difficult than they did two weeks ago at Old Trafford.
Even so, the visitors need more cutting edge in the final third if they are to pull off a shock victory tonight, having failed to really trouble Szczesny so far.
Ronaldo has just scored an absolute beauty to break the deadlock against his former club, lashing a stunning first-time volley past a helpless De Gea. Bonucci picked him out with a pass over the top, and Ronaldo watched it all the way over his shoulder before producing an unstoppable strike.
That is a huge goal for United, who are now just a few minutes away from a hugely impressive result in Turin!
Young swings a deep free kick into the box which Fellaini just cannot reach, but which still causes problems. Players are racing in on top of Szczesny, who can only parry it out against Bonucci, who is helpless the ball bounces off him and over the line.
It is a result every bit as impressive as their 3-2 win here in 1999 or their 3-0 triumph in 2003, and it is a much bigger shock than those two results as well!
Thank you very much for joining Sports Mole for tonight's match as Manchester United pull off a memorable comeback victory away to Juventus in Turin. 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!