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.
The Ayew brothers swapped half chances in the final 10 minutes before Andre had the final say with three minutes left.