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:
13. Bradley Dack (sub) - 7
Early stages of his cameo were his best in a Sunderland shirt, quickening up the play and finding team mates in good areas. Missed a good chance at the near post and gave it away a bit late on, but made a difference. 7 Photo: Frank Reid
14. Patrick Roberts (sub) - 7
Changed the complexion of the game by holding into the ball and pushing Millwall back. No goal contribution but undeniably important to the win. 7 Photo: Frank Reid
15. 1U6A3447.JPG
Really struggled to make an impact, just not able on this occasion to get hold of it. 4 Photo: Ian Horrocks