Villa midfielder Delph 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.
Villa knocked the ball around with confidence after Sunderland forced a couple of early corners and John O'Shea produced a crucial challenge to rob Weimann after Alan Hutton had cut the ball back to the Austria forward.
Bridcutt lasted only 18 minutes before 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.
Both sides lacked quality in the final third, but N'Zogbia forced Costel Pantilimon to make a save when he cut in from the right
Weimann 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.
Ron Vlaar rescued Villa with a fine last-ditch tackle on Wickham after Adam Johnson had picked the striker out with an incisive pass.
Sunderland had a spring in their step following Delph's sending off and Villa were indebted to a fine block from substitute Okore when Steven Fletcher's venomous strike looked destined for the back of the net.
Wickham somehow failed to open the scoring after 67 minutes following a goalmouth scramble as Villa struggled to get out of their own half.
Jack Grealish almost put the home side in front against the run of play, but his side-footed finish was just wide of the far post and Pantilimon produced a fine save to keep out a Vlaar header as Villa attempted to snatch a winner.
Brad Guzan got a fingertip to a left-foot strike from Gomez that 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 snatch all three points.
