United started strongly, carving out a couple of half-chances early on, but went into their shell as the half progressed. That allowed Partizan to grow into the game.
The hosts created plenty of chances of their own but failed to take advantage and found themselves 1-0 down against the run of play. It was Anthony Martial who converted from the spot after Brandon Williams was brought down in the box by Nemanja Miletic.
United entered the half-time break a goal to the good but Partizan shot out of the blocks in the second period, taking the attack to Ole Gunnar Solskjaer's side. They even had a couple of penalty shouts turned down as United continued to ride their luck.
The Red Devils then managed to withstand a late onslaught from the Serbian side to secure their first away win since March. That means they remain at the summit of Group L, two points clear of Alkmaar.
Here's a look at three players who impressed in the game, and two that didn't:
Impressed: Brandon Williams
19-year-old full-back Brandon Williams was handed a surprising start for Manchester United, and he grabbed his opportunity with both hands.
Although Williams looked shaky at the back initially, he was a force to be reckoned with going forward. The youngster won United's penalty in the first half after being brought down by Nemanja Miletic.
Williams received the ball near the byline and darted past a couple of challenges before being felled by Miletic inside the box.
He maintained a steady level throughout the 90 minutes and was arguably United's best player on the night.