Spain striker Fernando Llorente scored a double for Swansea in a precious 3-2 win over Burnley on Saturday overshadowed by a controversial penalty.
Llorente headed in the winner after 92 minutes after opening for the hosts on 12 minutes as Swansea pulled five points clear of the bottom three.
An Andre Gray double, either side of goals from Llorente and Martin Olsson, had looked like handing Burnley a first away win of the season.
But the match was overshadowed by a 20th-minute penalty awarded by referee Anthony Taylor for a handball in the box with replays showing the ball had actually come off the arm of Burnley's Sam Vokes.
Gray slotted in the resulting spotkick amid furious protests from Swansea players and manager Paul Clement.
Clement had made one change from last weekend's 3-1 defeat at Chelsea, with Dutch winger Luciano Narsingh handed his first start.
Burnley manager Sean Dyche made three changes from their 1-1 draw at Hull with Paul Robinson replacing Tom Heaton in goal and midfielder Jeff Hendrick and Wales striker Vokes starting.
Swansea's Alfie Mawson hit the woodwork twice in the opening minutes before Leroy Fer curled across to the onrushing Llorente who headed in from close range after 12 minutes.
After converting the penalty, Gray doubled his tally on 61 minutes with his eighth goal of the season after picking up a Vokes cross.
Just a minute later Olsson put Swansea back in the match as he finished off an extraordinary back heeled kick from Gylfi Sigurdsson.
But it was Llorente who once again proved Swansea's saviour after goals against Liverpool and Crystal Palace this season as he rose to head in the winner two minutes into injury time.
Burnley, who beat Swansea in their opening match of the season at home, have only claimed two points on the road, and are just four points ahead of Swansea in 12th.
The victory is a boost for Swansea's survival hopes with trips to Hull and Bournemouth to come and a home match against Middlesbrough.