The Norway international scored his 14th goal of the season as Villa again frustrated their fans.
Villa might be unbeaten at home this year but this was the seventh draw in 10 matches and their hopes of a top four spot are diminishing fast.
Sunderland, meanwhile, stretched their unbeaten run to five games as they continue to push themselves out of the relegation area.
As usual, Villa made their customary fast start with Ashley Young their main tormentor.
Goalkeeper Craig Gordon, who thwarted Birmingham City on Saturday, maintained his impressive form for the Black Cats.
Twice in quick succession the Sunderland goalkeeper denied Villa goals with two saves with his legs.
On the first occasion he kept out a rasping drive from Young and then saved a James Collins header again with his legs.
Sunderland managed to get the ball into the net but Darren Bent's effort was ruled offside.
But in the 13th minute, Villa suffered a major setback when Emile Heskey limped out of the game to be replaced by Nathan Delfouneso.
Sunderland's goal continued to enjoy a charmed life with Collins going close with another header from a Young cross.
But in the 22nd minute the Villa fans were stunned when the two former Manchester United players, Kieran Richardson and Fraizer Campbell, conspired to open the scoring for the visitors.
Richardson pierced Villa's defence with a throughball and Campbell raced past Collins to score with a low shot to the left of goalkeeper Brad Friedel.
This setback only spurred Villa to greater efforts and in the 30th minute they were rewarded when the best move of the goal resulted in a Carew grabbing the equaliser.
James Milner sent Young clear on the right and he produced another fast cross which Carew converted with his long outstretched leg.
In an even second half, Sunderland, who have not won away from home since the opening day of the season, should have notched a second goal.
John Mensah was so surprised to find himself completely unmarked in the six-yard box that he headed Richardson's cross wide of the goal.
The closest villa came to a claiming the winner occurred when Carew headed over from a Stewart Downing cross.