Samba was given a straight red card for pulling down Danny Welbeck in the 45th minute as the Sunderland forward was about to break into the area.
Sunderland striker Darren Bent wasted the best chance of the game midway through the first half when he came one-on-one with Paul Robinson but fired a weak shot straight at the goalkeeper.
Under a persistent rain at Ewood Park, Bent had another chance early in the second period when he met a cross from Ahmed Elmohamady but sent his close-range header well wide.
Both teams have 9 points from eight games.