First-half goals from John McGinn and Leander Dendoncker would seemingly prolong the Red Devils' festive misery, but as the title-chasing Lions took their foot off the gas, Alejandro Garnacho clawed the hosts back into the game with a brilliant brace before Hojlund completed an astonishing turnaround with his maiden goal in England's top flight.
Recalls for Marcus Rashford and Christian Eriksen headlined the team news from the Man United camp, while Diego Carlos was reinstated to the Villa XI in place of the banned Matty Cash.
Following confirmation of Sir Jim Ratcliffe's 25% purchase, Ineos director of sport Sir Dave Brailsford was in attendance at Old Trafford, but he cut a glum figure as Erik ten Hag's men produced another worrying first-half display.
Neither side really took the game by the scruff of the neck in a cagey start to proceedings, but the Red Devils were undone by a set piece in the 22nd minute, where McGinn set the ball down on the left-hand side a fair distance away from goal.
The Scotsman's inswinging delivery missed everyone, bounced once and deceived Andre Onana before nestling into the side of the net, and Man United's appeals for offside against Ollie Watkins - who tried to get a nick on the ball but failed to do so - fell on deaf ears.
If Man United's defending was questionable for Villa's opener, their attempts to prevent Unai Emery's men from doubling their lead just five minutes later was nothing short of abysmal, as Clement Lenglet nodded a McGinn corner back into the mixer, where Dendoncker was left unmarked to skilfully flick the ball home with a backheel volley.
No fewer than three Man United bodies were on the line, but not a single one was picking up Dendoncker, and a cacophony of boos soon erupted in the direction of Ten Hag's directionless side.
Having belatedly been shaken awake, Man United started to force the issue a bit more in the dying embers of the opening period, starting with Marcus Rashford shooting straight at Emiliano Martinez in the 32nd minute.
However, the bulk of the hosts' forward forays ended with a poor final ball or Villa's high line catching the Red Devils' attackers offside, although Rashford did produce a burst of pace to get away down the left in added time, only to slice his close-range effort behind.
The Red Devils remained in the ascendancy as the second half got underway and thought that the deficit had been cut in half in the 48th minute, as Garnacho skipped past Martinez and finished into an empty net after Man United played out from the back expertly.
Both Rashford and Garnacho had left all 10 Villa outfielders in their wake, but the latter had gone too early - failing to stay behind the ball as Rashford played the pass - and Man United's lifeline was extinguished.
It only took another 11 minutes for the same combination to produce the same result, though, and there was no denying Garnacho his rightful goal this time around, as Rashford squared for the 19-year-old to get the hosts back into the game with a first-time finish across goal.
Garnacho's response ended Man United's seven-hour goal drought dating back to their 2-1 win over Chelsea 20 days ago - Lucas Digne injured himself in the process of trying to stop it - but it took a strong hand from Onana to prevent Leon Bailey restoring the Lions' two-goal lead within a minute of the restart.
All in all, though, Emery's team were a shadow of their former selves, and the resurgent Red Devils drew themselves level in the 71st minute, as Garnacho bagged his second of the night in fortuitous circumstances.
A low Bruno Fernandes cross from the right wing took a nick off of Lenglet's toe into the path of Garnacho, who created the angle for the shot in a central position, and his effort took a significant deflection off of Carlos to dupe a diving Martinez.
Once again, Villa came up with an incredibly brief response to the Argentine's strike, as McGinn found himself with time and space to let fly inside the box in the 72nd minute, but his tame goal-bound effort was hacked clear by Jonny Evans.
Ten Hag's side soon began to huff and puff again, and after failing to deal with two crosses for Villa's two first-half goals, Man United came good from their own set-piece to complete an astounding turnaround.
Another Fernandes delivery from the right did the damage, as the Portuguese's corner bounced off of McGinn's knee into the path of Hojlund, who showed brilliant reactions to side-foot a volley into the net via the post for his inaugural Premier League goal.
The 20-year-old Danish starlet could not hold back months of pent-up emotion - his face was almost as red as his shirt as he let out roar after roar - and nor could tens of thousands of fans inside the Theatre of Dreams, although glee turned into groans when nine minutes of added time were announced.
Emery's side had nothing left to give, though, as Man United leapfrogged Brighton & Hove Albion into eighth place in the table, while Villa remain in third, having missed the chance to rise above Arsenal into the runners-up spot.
A trip to Nottingham Forest on Saturday represents Man United's final fixture of a turbulent 2023, while Villa are at home to Burnley on December 30.