Chris Samba saw red in first-half stoppage time after bringing down Danny Welbeck just before the Black Cats forward could burst into the box.
Darren Bent, who started the game having shaken off the injury which forced him out of England's match against Montenegro, had earlier wasted a glorious chance to open the scoring, and the visitors were unable to make their man advantage count after the break as it finished all square.
Both sides have struggled for goals this season and there was little here to suggest that is going to change any time soon.
After a scrappy opening, Ahmed Elmohamady guided a header into Lee Cattermole's path, who cut into the box and went down claiming Gael Givet had fouled him. Referee Lee Probert waved play on, with replays suggesting any contact had been minimal.
Morten Gamst Pedersen nearly opened the scoring around the quarter-hour mark with a swerving, dipping free-kick that Simon Mignolet - again preferred in goal for the Wearsiders to Craig Gordon - managed to tip over the bar.
Moments later El-Hadji Diouf sent a low cross into the danger zone which Titus Bramble intercepted, before Welbeck saw an acrobatic attempt go well wide.
Bent then squandered a good opportunity, the Black Cats' top scorer latching on to a long ball after a mistake by Gael Givet but shooting weakly at Paul Robinson in a one-on-one situation.
Pedersen called Mignolet into action again with another free-kick from almost the same position as before, the Belgian keeper getting his fist to the delivery.
Diouf was next to send a useful ball into the box which Nikola Kalinic headed the wrong side of the post.
The Senegalese player then showed his more petulant side, raising his hand to Phil Bardsley's face and fortunate to get away without a booking.
There was no such respite for Samba in first-half stoppage time though after he brought down Welbeck just outside the box.
The Rovers skipper was given his marching orders, with Bardsley striking the resulting free-kick against the wall and Bent firing the rebound wide.
Bent misdirected a header from Elmohamady's cross at the start of the second half, while Pedersen's free-kick caused a scramble in the Sunderland box which neither Kalinic nor Jones could finish off.
Both managers attempted to bolster their attacking options by throwing on forwards, with the Black Cats' record signing Asamoah Gyan replacing Nedum Onuoha.
Rovers boss Sam Allardyce introduced Benjani Mwaruwari for Kalinic, as well as David Dunn, who came on in place of Michel Salgado.
The visitors had a chance soon after as Robinson rushed out to slide the ball away from Bent. It fell to Steed Malbranque but the Frenchman could not get his effort on target.
Benjani wriggled free and unleashed a shot that soared high and wide and Bramble was also unable to find any accuracy with a volley.
Diouf then almost managed to get on the end of a weak back-pass by Elmohamady but Mignolet arrived in time to beat him to the ball.
Benjani had to come off after picking up a knock and Mame Biram Diouf was sent on, while Boudewijn Zenden, who had come on for Malbranque, got a header on target which Robinson saved.
The newly-introduced Diouf tried a snapshot that did little to trouble Mignolet and Gyan went closer with a curling shot that slipped narrowly wide.
Zenden also had a speculative shot towards the end but the game had been petering out for some time by then and a 0-0 draw seemed the only fair result by the final whistle.