Bruno Fernandes opened the scoring for United, but goals from Florenzo Pellegrini and Edin Dzeko left Ole Gunnar Solskjaer’s Red Devils trailing 2-1 at the interval.
Unfortunately for Roma, United turned on the style after the break with five second-half goals from Edinson Cavani (two), Fernandes, Paul Pogba and Mason Greenwood to take a four-goal cushion into the second leg.
Watch: Ole Gunnar Solskjaer says Man United must listen to fans' views ahead of protest
Man Utd player ratings
David De Gea 6
Could do little about either Roma goal, but a nervy kick against Edin Dzeko early in the second half shows why he is currently No2.
Aaron Wan Bissaka 6
Grew into the game as it progressed, with his shot on the overlap leading to Cavani's second goal.
Victor Lindelof 6
A tough night against Dzeko, with the Roma striker bossing United's defence for stretches.
Harry Maguire 6
Was caught flat-footed on more than one occasion by Dzeko and Pellegrini, but battled back and was solid after the break.
Luke Shaw 6
Not up to his usual standards at the back, playing Pellegrini on for Roma's second goal - but his attacking play after the break kept the visitors pinned back.
Once again suffered with Rashford posted out on the opposite flank.
Scott McTominay 6
Was caught once or twice on the ball before the break with United struggling for shape, but looked far more composted with the team on the front foot.
Another solid midfield display from the Brazilian - kept things tight as United dominated after the break.
Marcus Rashford 6
Another example of why the right flank doesn't suit him, though Pogba's fine performance suggests Rashford may be a potential casualty of that tactical switch in big games.
His replacement, Greenwood, looks far better on the right, and scored soon after coming on.
Bruno Fernandes 9
His early goal was brilliantly taken, and he led by example after the break with two assists for Cavani and a penalty.
A sensational after a recent barren run by his own high standards, and his partnership with Pogba looks promising.
Paul Pogba 9
Conceding a penalty for a needless handball aside, this was a top performance from the World Cup winner.
Roma couldn't handle him, and a powerful header - his first goal at Old Trafford for two years - was just reward.
Edinson Cavani 9
What more can you say? An all-round striker's performance, with two well-taken goals, an assist for Greenwood, and technically another one for winning a penalty.
Movement, power, and clinical finishing - he's still got it.
Mason Greenwood (Rashford, 76') 7
Another impressive cameo, scoring off the bench to add to his growing tally. Replaced Rashford, and is making a case to be starting ahead of the former on the right flank during the run-in.
Juan Mata (Fernandes, 89') N/A
Nemanja Matic (Fred, 83') N/A
Subs not used: Bailly, Grant, Diallo, James, Henderson, Alex Telles, Williams, van de Beek, Tuanzebe
Watch: 10 Minute Core Home Workout Without Equipment | Move At Home