Christopher Samba was shown a red card just before half-time for Rovers after tangling with Danny Welbeck but the hosts hung on for a 0-0 draw in a desperately disappointing game.
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Darren Bent had Sunderland's best chances, wasting a one-on-one opportunity in the first half and then making a hash of a headed opportunity in the second.
Sunderland's record signing Asamoah Gyan came off the bench in the second half and the Ghana international forced a diving save from Rovers keeper Paul Robinson late on.
Both sides remain in the bottom half of the table with nine points.
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