Having recorded a goalless draw in the first leg in France, United got off to the perfect start when Ryan Giggs found Wayne Rooney and the England striker’s shot across the face of goal was turned in by Javier Hernandez.
Marseille should have levelled matters moments later but Andre-Pierre Gignac cleared the crossbar after being put one-on-one with veteran United goalkeeper Edwin van der Sar.
The hosts’ hopes of reaching the last eight were dealt a setback when, already without Nemanja Vidic and Rio Ferdinand, they lost John O’Shea to a hamstring injury.
Their makeshift defence hung on as Souleymane Diawara failed to test van der Sar with a header, and former defender Gabriel Heinze was the next man to scare the Old Trafford faithful when he headed wide.
Wes Brown almost sliced the ball into his own net before Rafael, who had earlier replaced O’Shea, had to be stretchered off with what appeared to be a hamstring problem.
Van der Sar saved well from Benoit Cheyrou as Marseille continued to pile forward in search of a crucial away goal, and Hernandez then ensured they would need two goals when, with 15 minutes to go, he slotted home United’s second after good work from Antonio Valencia and Giggs.
The Red Devils gifted their visitors a lifeline with seven minutes remaining when Brown diverted an Lucho Gonzalez corner into his own net despite the best efforts of Paul Scholes, but the Premier League leaders held on to book their pace in the last eight.