Fernando Llorente scored deep into injury time to see off a resilient Burnley and claim a dramatic 3-2 win for Swansea City.
The Spaniard gave the hosts an early lead after dominating the opening 13 minutes, which included hitting the woodwork twice, with the striker latching on to Leroy Fer's cross to head home.
Earlier, Andre Gray's double looked like handing Burnley some rare away-day joy. But the contest will unfortunately be remembered for the 20th-minute penalty Burnley were awarded when George Boyd's corner escaped everyone before striking the arm of Clarets striker Sam Vokes.
Television replays showed Swansea's Gylfi Sigurdsson appealing for handball against Vokes, and there did not appear to be any other offence in a congested six-yard box.
But Taylor incensed Swansea players by pointing to the spot and Gray's straight-down-the-middle kick cancelled out Llorente's 12th-minute header.
Gray put Burnley ahead just after the hour mark with his eighth league goal of the season before full-back Olsson scored for the second successive home game to get Swansea back in the game and set up a grandstand finish which allowed Llorente to grab the late winner.
Swansea's fast start was almost rewarded when they struck the woodwork twice in the same 11th minute attack.
Alfie Mawson headed Sigurdsson's free-kick against the crossbar and, following some pinball in the Burnley ball, the centre-back was denied for a second time when his shot cannoned back off a post.
Burnley were only granted a short reprieve as Llorente met Leroy Fer's cross at the far post a minute later to head home his 10th goal of the season.
Burnley responded well to that setback as Jeff Hendrick fired into Lukasz Fabianski's midriff before their controversial leveller from the spot.
The sense of injustice that decision created seemed to drive on a Swansea side who should have been ahead before the break.
Paul Robinson, deputising for the Clarets' regular goalkeeper Tom Heaton, who was missing through illness, batted away Martin Olsson's drive before Sigurdsson flashed a drive inches wide.
Swansea then struck the woodwork for the third time when Llorente's header bounced back off the crossbar and the half closed with Robinson pushing aside Sigurdsson's free-kick.
Burnley's goal was leading a charmed life and Ben Mee made a goal-line intervention from Sigurdsson at the start of the second half.
Llorente then went close again, not quite managing to get enough purchase on a Tom Carroll centre, but Swansea were stunned after 61 minutes when Vokes beat Federico Fernandez in the air.
The ball dropped to the unmarked Gray and he had time to turn and deliver a shot past Fabianski and gave Burnley real hope of a first Premier League away win since May 2015.
But Swansea were level within six minutes as Sigurdsson slipped in Olsson and his powerful angled finish into the roof of the net gave Robinson no chance.
Carroll almost won it when his goalbound shot was turned off the line by Mee, but the midfielder soon swung over a cross, with two minutes of injury time on the clock, and there was Llorente to rise superbly and spark wild Swansea celebrations which included a touch-line dash from boss Paul Clement.