Allback scored his fourth goal in four games just 10 minutes from time to earn Villa only their second win in their last 11 games. His strike also sent luckless Sunderland crashing to their 14th successive defeat.
Their latest defeat has also condemned Sunderland to being relegated with the lowest ever points tally in Premiership history.
With Villa's Premiership status on the line, they made a predictably nervy start and Sunderland were unfortunate not to take control.
Villa goalkeeper Peter Enckelman did well to beat away a shot from Kevin Kyle after just three minutes and then had to be alert again to push a 30-yard drive from Gavin McCann over the bar five minutes later.
But Villa should really have settled their nerves in the 11th minute when Allback was presented with a golden chance by his strike partner, Darius Vassell.
Vassell released Allback only for the Swede to drag his shotacross the face of goal from 14 yards.
While Villa continued to press through Allback, it was Sunderland who looked more threatening only to again be denied by Enckelman.
A misplaced pass by Villa skipper Steve Staunton in the 24th minute allowed Kevin Phillips to break clear.
He swept past the challenge of full-back JLloyd Samuel only to be denied by a finger tip save from Enckelman.
Clear-cut chances proved hard for Villa to create, but central defender Ronny Johnsen was presented with a golden opportunity to break the deadlock 12 minutes before half time.
He was picked out at the far post by a free kick from Staunton only to blaze his shot from six yards over the bar.
It threatened to be a costly miss as only the woodwork prevented Sunderland taking a deserved lead 14 minutes into the second half.
A sweeping cross from Gavin McCann fell to the left foot of Kyle but he could not keep his shot down and it bounced to safety off the top of the bar.
In a desperate bid to try and secure the win that would make his side safe, Villa boss Graham Taylor took off midfielder Lee Hendrie and sent on striker Dion Dublin to form a three man front-line alongside Allback and Vassell.
But it was Sunderland who continued to carry the greater threat and their pressure should final have paid dividends after 75 minutes.
With Villa appealing for offside, Phillips nodded the ball into the path of the unmarked Kyle who, faced with just Enckelman to beat, somehow managed to pull his shot wide.
That finally proved the let-off that sparked Villa into life and Allback was able to complete a smart three-man move to secure their place in the Premiership.
Midfielder Ian Taylor fed the ball into the path of Joey Gudjonsson who released Allback.
Allback then held off the challenge of two Sunderland defenders before firing past Mart Poom from ten yards.