The England midfielder was sent off in the opening stages of the second half but Paul Lambert's men stood firm to take a point from their clash with the Black Cats
The England midfielder was shown a straight red card by referee Martin Atkinson for a late challenge on Jordi Gomez just four minutes into the second half.
It was the third time in the last four Premier League games that Paul Lambert's side had been reduced to 10 men, but Sunderland were unable to make the most of their numerical advantage.
Gus Poyet's side had their chances after Delph's dismissal, with Gomez striking the post late on, but Villa dug deep and showed plenty of character as they held on for a point.
Villa's lack of goals will be a concern for Lambert, as his side have only found the back of the net 11 times in 19 top-flight games, while Sunderland have won just one of their last nine matches.
Andreas Weimann was recalled to the Villa starting line-up to replace the suspended Gabriel Agbonlahor, while Charles N'Zogbia started at the expense of Jores Okore.
Sunderland striker Connor Wickham returned from suspension, with Wes Brown and Liam Bridcutt also starting as Ricky Alvarez, Lee Cattermole and Sebastian Coates dropped to the bench.
Bridcutt lasted only 18 minutes, though, as he was replaced by Cattermole after failing to recover from a collision with Christian Benteke.
Wickham has scored only two Premier League goals this season, but the striker was clearly not short of confidence as he tried his luck with a curling effort that flashed wide of the far post shortly after.
Both sides lacked quality in the final third, but N'Zogbia forced Costel Pantilimon into a good save when he cut in from the right.
Weimann then failed to punish Sunderland when they lost possession in their own half, dragging a poor finish wide of the far post with his left foot.
There was finally a talking point in an uneventful match early in the second half, when Delph was given his marching orders by referee Atkinson for a poorly timed tackle on Gomez.
Villa were then forced to retreat, and Wickham somehow failed to open the scoring after 67 minutes following a goalmouth scramble as Villa struggled to get out of their own half.
Wickham was almost punished as Jack Grealish broke quickly, but his side-footed finish was just wide of the far post and Pantilimon then produced a fine save to keep out a Vlaar header as Villa attempted to snatch a winner.
Gomez rattled the post and Pantilimon denied Leandro Bacuna before Benteke headed into the side-netting in stoppage time in a dramatic finale, but neither side could take all three points.