After a goalless first half, Lions defender Jake Cooper opened the scoring just before the hour mark after a corner.
The Black Cats then managed to equalise nine minutes from time when Alex Pritchard’s free-kick was converted by Dennis Cirkin.
Mowbray’s side will now prepare for next week’s FA Cup replay against Fulham.
Here’s how Phil Smith rated the Sunderland players against Millwall:
9. Adil Aouchiche - 5
Started really well, getting a lot of touches and conducting the play. Teed Neil up for a couple of efforts, but started to lose the ball too often and so replaced by Pritchard early in the second half. 5 Photo: Frank Reid
10. Jack Clarke - 6
Had a poor first half by his standards, unable to make the most of some promising chances to break at goal. His persistence paid off though, winning a penalty and scoring his tenth goal of the season from the spot. 6 Photo: Frank Reid
11. Mason Burstow - 4
Started brightly but faded as the first half went on and after picking up a yellow card for a late challenge. Couldn’t hold it up against Millwall’s physical central defenders and replaced just after the break. 4 Photo: Frank Reid
12. Alex Pritchard (sub) - 7
His ability to get on the ball and hold it gave Sunderland a foothold in a game that was passing them by. 7 Photo: Frank Reid