The Black Cats had a strong appeal for a penalty when Jack Clarke tangled with defender Ryan Hedges but nothing was given.
Rovers then immediately broke forward and opened the scoring after an excellent strike from Ben Brereton Diaz from the edge of the box.
The hosts doubled their lead when Scott Wharton converted Hedges’ free-kick with a glancing header.
Our Sunderland writer Phil Smith has dished out his player ratings from Ewood Park:
1. Anthony Patterson - 5
Will be disappointed to be beaten from such a narrow angle for the second but replays suggested there was an offside just in front of him. Distribution was very erratic late on. 5 Photo: Martin Swinney
2. Luke O’Nien - 6
Drove forward when he could and battled against an excellent opponent in Ben Brereton Diaz for the most part. Got into some good areas late on to no avail. 6 Photo: Frank Reid
3. Danny Batth - 6
Went close with a header in the second half and made some very important defensive contributions without. Couldn’t say he did much wrong despite the defeat. 6 Photo: Frank Reid
4. Aji Alese - 6
Looked sharp and defended well before being forced off midway through the second half having come off the worst in a 50/50 challenge. A significant concern for Sunderland given his superb form of late. 6 Photo: Frank Reid