Paul Pogba came off the bench at half-time and scored in the 48th minute. With the win, the Red Devils entered tomorrow's hat for the last-8 draw.
Having thrown up a stern challenge in the first-leg at Old Trafford, the Rossoneri produced a limp display tonight.
That energy, spirit, and effervescence was completely absent from their game and even the introduction of star man Zlatan Ibrahimovic couldn't spark a comeback.
Milan sure amped up the pressure in the dying moments but could never really carve out decent opportunities.
Manchester United went through as deserved winners and will learn their next opponents tomorrow.
Manchester United and AC Milan hits and flops from the match:
Hit: Paul Pogba (Manchester United)
Now that's the kind of impact which Manchester United fans have been desperately waiting to see from Paul Pogba.
Coming on at the break to replace Marcus Rashford, the Frenchman scored just three minutes into the restart to put United in front.
A penalty box scramble saw the Rossoneri fail to clear their lines before Pogba, from a tight angle, lifted an audacious effort over Donnarumma.
Having only returned from a hamstring injury, the 28-year old got his first slice of Europa League action of the season and marked the same with a match-winning goal.
Pogba, if he remains fit hereafter, could play a key role in United's title charge in the competition.
Flop: Hakan Calhanoglu (AC Milan)
Having missed the first-leg of their clash at Old Trafford, Hakan Calhanoglu's return to the fold was expected to bolster their hopes tonight.
But the Turkish international had a whimper instead and failed to stamp his authority in the game.
He wasn't terrible by any means, even making a few good crosses, one of which saw Ibrahimovic get a head to it and force a fine save from Dean Henderson.
However, when you're the number 10 of the side and often the creator-in-chief, expectations riding on your shoulders will also be pretty high.
Unfortunately, Calhanoglu didn't live up to them tonight.