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.
1. Anthony Patterson - 8
The main reason his team were able to get a point in the end. Made two superb stops to deny Bradshaw, one a reflex effort at his near post and one a very good 1-v-1 stop. 8 Photo: Frank Reid
2. Trai Hume - 5
Like most of Sunderland’s defence he looked a little laboured in and out of possession, with a tough week perhaps catching up. Millwall had some big chances. 5 Photo: Frank Reid
3. Dan Ballard - 5
Made one fine challenge to deny Nisbet but was caught out too high up the pitch for the goal. Not quite at his commanding best, but won a lot of headers. Sunderland looked uncertain throughout. 5 Photo: Frank Reid
4. Luke O’Nien - 5
Started well on the ball, playing some excellent switches of play to Clarke. Ultimately there were too many errors across Sunderland’s backline, on an afternoon when they needed their goalkeeper in the end. 5 Photo: Frank Reid