The 2-2 draw, with Stoke cancelling out their hosts' 2-0 lead in the final three minutes, left fourth-placed Villa six points ahead of Arsenal and three adrift of second-placed Chelsea and Liverpool in the Premier League.
Champions Manchester United, who beat holders Tottenham Hotspur on penalties in Sunday's League Cup final at Wembley, are seven points clear at the top with a game in hand.
Arsenal, who beat AS Roma 1-0 in the Champions League in midweek, had stumbled to a 0-0 draw at home to Fulham on Saturday.
Bulgarian Stilian Petrov put Villa ahead on the stroke of halftime and John Carew added the second in the 79th, only three minutes after replacing Emile Heskey.
Stoke then grabbed what looked like a consolation goal through Ryan Shawcross in the 87th before Glenn Whelan struck the equaliser in stoppage time.
"It's desperately disappointing," Villa manager Martin O'Neill, who rested several key players after their UEFA Cup last-32 defeat by CSKA Moscow on Thursday, told Sky Sports television. "We got a bit slack."
DEEP TROUBLE
The draw still left Stoke deep in trouble, dropping to 19th place after Blackburn Rovers beat Hull City 2-1 to claw their way out of the bottom three on goal difference.
Hull and Blackburn both ended their match with 10 men after the home side's Dean Marney was sent off in the 63rd and Blackburn's Morten Gamst Pedersen followed eight minutes later for a second booking.
Blackburn also scored twice in quick succession, taking the lead in the 34th when Roque Santa Cruz punished an error by goalkeeper Matt Duke and set up Stephen Warnock to side-foot into the top of the net.
Warnock then crossed from the left for Keith Andrews to tap home. Hull pulled a goal back through Ian Ashbee in the 79th.
Blackburn moved up to 17th place on 26 points, ahead of Middlesbrough on goal difference.
