Andre Ayew bagged a late winner as the Swans claimed a 2-1 victory to seal a first win since August and ease any pressure on manager Garry Monk.
But Sherwood is now under immense scrutiny at Villa after they blew a second-half lead to continue their winless run.
Villa have won just once in the Barclays Premier League this season and remain stuck in the drop zone, four points from the safety line, following a sixth straight league defeat.
Jordan Ayew's first goal for the club was cancelled out by Gylfi Sigurdsson's excellent free-kick and Sherwood's job is now in serious danger.
It was a dramatic end to a terrible game but at least Swansea will take solace after they ended a six-match winless streak.
The first half was littered with errors and sloppy play but Federico Fernandez should have fired Swansea ahead after 13 minutes.
Villa had looked suspect at set-pieces and the Swans nearly cashed in from one Jonjo Shelvey delivery only for Fernandez to balloon over from Bafetimbi Gomis' knockdown.
There was barely any edge to a tepid game, with Swansea unable to flow in the face of Villa's gritty, if predictable, efforts.
Aside from comfortably claiming free-kicks from Kieran Richardson and Leandro Bacuna, Swans goalkeeper Lukasz Fabianski had little to do.
The only serious action in his area came after half an hour when Micah Richards and Fernandez squared up, prompting Ashley Williams to confront Richards.
The Wales defender and Richards were booked but it at least brought a dire game to life.
Rudy Gestede headed Bacuna's corner over soon after in Villa's best chance of the half but they wasted a fine opening minutes after the restart.
Swansea were still sleeping when Jack Grealish broke and found Agbonlahor but the forward shot wide with Ayew free in the area.
Villa had upped their game but Gomis escaped their attention on 59 minutes only to drag his angled effort wide.
The game had sparked to life and it then exploded after two moments involving brothers Andre and Jordan Ayew.
First, Swansea's Andre Ayew was denied by a fine point-blank save from Brad Guzan after the keeper rushed out to block the striker's effort from Gomis' cross.
Instantly, Villa broke and Agbonlahor worked his way into the area to set up Jordan Ayew, who was left free at the far post to head in for a 62nd-minute opener.
However, Villa's lead lasted just six minutes when Richards brought down Sigurdsson and the midfielder brilliantly curled into the bottom corner from 25 yards.
It took the sting out of Villa and they struggled to break down the well-drilled Swans.
The Ayew brothers swapped half chances in the final 10 minutes before Andre had the final say with three minutes left.
Villa were too open on the right and allowed Kyle Naughton to cross for Andre Ayew to convert from close range.
It was a damming blow for Villa and there seemed to be drama after the final whistle as the players came off, with the tunnel rocking from side to side forcing stewards to rush in.
Source : PA