Gus Poyet's side are winless on the road this season but did pick up their first away point since the 1-1 draw against Southampton in August.
They should have left Villa Park with all three, Emanuele Giaccherini hooking the ball over the bar from point-blank range at the end of the first half when it looked easier to score.
The hosts had slightly the better of a dour affair, but again it was the visitors who came closest to scoring in the second half, Fabio Borini striking the crossbar with a header in the 67th minute.
The hosts made four changes from Monday's draw at West Brom, with Gabriel Agbonlahor and Andreas Weimann among those to return to the side following injury, while Poyet made three alterations as Andrea Dossena, Craig Gardner and Borini all came in.
Agbonlahor threatened twice inside the opening five minutes, glancing a header wide before curling a low shot from the edge of the box that was comfortable for Vito Mannone.
Goalmouth action was scarce in a turgid opening half hour, Christian Benteke steering his effort a yard over the bar after being teed up by Ashley Westwood in the 29th minute.
Sebastian Larsson whipped a free-kick narrowly wide of the post four minutes later after Dossena had been fouled by Ron Vlaar on the corner of the box.
Former Villa man Gardner did have the ball in the net after 41 minutes, but the goal was rightly disallowed as the midfielder had received the pass in an offside position.
Giaccherini then spurned a golden opportunity on the stroke of half-time as the Italian somehow turned the ball over the bar from two yards after being picked out by Phil Bardsley's knock down.
Villa started the second half the stronger, Mannone beating away Agbonlahor's drive at the near post four minutes after the restart, before Westwood curled a shot straight at the goalkeeper from 25 yards.
Midway through the half, Borini met Giaccherini's left-wing cross firmly, only to see his glancing header crash off the bar and away to safety.
It was the last action of note, both sides struggling to create chances in the final stages as Sunderland made it five away games without a goal, although the draw did end a run of five consecutive away league defeats for Poyet's side.
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