The Red Devils went for Alex Telles at full-back and kept Dean Henderson in goal from Sunday's Manchester derby win, as Milan missed star man Zlatan Ibrahimovic.
Milan set off the quickest after Rafael Leao pounced on an error from Harry Maguire to fire in from the near side, but he saw the goal disallowed for offside.
The Rossoneri were denied the lead again 10 minutes in after Franck Kessie volleyed home, but the Video Assistant Referee (VAR) checked and called a handball on the Ivorian.
United managed to get in their own with a looping free-kick from Telles shortly before the half-hour mark, but Milan still saw inviting chances through Alexis Saelemaekers in particular.
The Red Devils missed a big chance in the last seven minutes to halftime when Maguire deflected Bruno Fernandes' flick-on against upright with the net gaping.
Ole Gunnar Solskjaer introduced a fresh face up front ahead of the second half in Amad Diallo, who replaced Anthony Martial.
It proved to be a masterstroke five minutes in as Diallo broke behind the defensive line to head a pin-point ball down the middle from Fernandes past goalkeeper Gianluigi Donnarumma.
Kessie almost handed the Serie A giants a way back minutes later with a snap-shot on the near side following a cutback by Saelemaekers, but Henderson pushed away.
United should've had a second from a clear opening on the far side but with 20 minutes to go, Daniel James dragged Mason Greenwood's ball wide.
Stefano Piolo's men threw bodies forward late on and were rewarded when Simon Kjaer headed home a corner to see a stalemate in Manchester.