Gerard Houllier's side slipped into the relegation zone on goal difference as a result of Wolves' shock victory over champions Chelsea at Molineux.
Villa had striker Emile Heskey sent off for violent conduct before Bardsley's decider and then Black Cats substitute Boudewijn Zenden was given his marching orders for two bookable offences.
A small section of Villa fans chanted "you're getting sacked in the morning" towards Houllier after Bardsley had broken the deadlock.
But the calls for Houllier to go were more intensified at the final whistle.
The last time Villa were in such a lowly position was in November 2003 during David O'Leary's reign as manager.
But Sunderland's second away win of the campaign keeps them on course for a European spot.
The first chance fell to Sunderland midfielder Steed Malbranque after Carlos Cuellar failed to make contact with a deep cross from Bardsley.
But Malbranque failed to test Brad Friedel with his header which drifted a couple of yards wide.
Kieran Richardson became the first player to be yellow carded after five minutes when he brought down Villa striker Emile Heskey in full flight.
Villa started to exert some pressure and Sunderland keeper Craig Gordon did well to finger-tip away a Stewart Downing free-kick under pressure.
A fine pass from Villa skipper Stiliyan Petrov allowed Nigel Reo-Coker a run at goal but he was halted by Malbranque's challenge.
Reo-Coker then played in Ashley Young but his first touch was not the best and Craig Gordon was able to collect.
Bardsley produced a fine tackle inside his own box to deny Heskey after he had made a powerful run.
Ciaran Clark became the first Villa player to be yellow carded after 29 minutes for a reckless challenge on Jordan Henderson.
Clark's mistimed pass then almost proved costly as it was seized upon by David Meyler but Darren Bent was unable to make the most of his pass.
Sunderland were forced into a change after 38 minutes when Meyler pulled up suddenly, slumped to the ground and had to be stretchered off and he was replaced by Zenden.
Heskey, who played under Bruce at Birmingham and Wigan, was guilty of a glaring miss five minutes before half-time.
Downing did well to get to the by-line and shake of Zenden's challenge before sending a low ball across the box.
Heskey seemed certain to score but, from three yards out, he shot against the crossbar.
Sunderland skipper Titus Bramble was booked for holding back Heskey and the Villa striker then headed wide from Young's cross when well placed.
James Collins was booked in injury-time for a challenge on Danny Welbeck.
There was a quiet start to the second period but Malbranque could have broken the deadlock after 50 minutes.
Collins' clearing header lacked conviction and was nodded back down by Bent to Malbranque who volleyed over from eight yards out.
Collins came to the rescue in atoning for his own error three minutes later. He was shaken off the ball by Bent who went around Friedel but Collins recovered to block his shot on the line.
Sunderland were now in the ascendancy and Cuellar diverted a goalbound shot from Malbranque around the post.
But Sunderland were the more threatening and Friedel got his body behind Welbeck's stinging low drive.
Zenden was yellow carded for bringing down the powerful Heskey but Villa were reduced to 10 men after 68 minutes when Heskey was sent off.
Henderson appeared upset Heskey did not put the ball out of play so Asamoah Gyan could have treatment.
He responded by shoving Henderson in the face and was given his marching orders by referee Peter Walton.
With 10 minutes left Bardsley broke the deadlock with a low 25-yard drive after Zenden's free-kick had been blocked.
Welbeck was stretchered off after 83 minutes and replaced by Cristian Riveros.
Zenden was also sent off for a second bookable offence when he fouled Stiliyan Petrov two minutes later.