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:
5. Niall Huggins - 6
Struggled to contain Norton-Cuffy at times in the first half and couldn’t get forward. Better late on when he had the likes of Pritchard to bounce off. 6 Photo: Frank Reid
6. Dan Neil - 5
Had Sunderland’s only real efforts of note in the first half, firing over the bar from the edge and then straight at Bialkwoski. Showed good work rate to try and press but quieter than usual on the ball. 5 Photo: Frank Reid
7. Pierre Ekwah - 5
Started very well but fell off the pace towards the end of the half as Millwall took control. Much better in the second half, keeping the ball and helping his side find their feet. 5 Photo: Frank Reid
8. Abdoullah Ba - 4
Couldn’t get into the game at all and lost the ball in some dangerous areas as the first half progressed. Replaced shortly after the break. 4 Photo: Frank Reid