The brilliant Joel Campbell opened the scoring, but Wayne Routledge's equaliser restored parity at the half-time break.
Swans captain Ashley Williams then bundled the ball home midway through the second half as the Gunners' title bid suffered a big blow.
Petr Cech 5 - Blameless for the first goal but the ex-Chelsea goalkeeper could, and definitely should, have been braver when coming for the cross which led to Swansea's second. Brilliant all season for the Gunners, but that was a big, big error.
Hector Bellerin 6 - He was not quick enough to react to Routledge's run which led to the equaliser, and his final ball left a little to be desired at the other end.
Per Mertesacker 5 - The big German dealt with Gomis relatively well, though his positioning was also questioning for Routledge's goal. He was lucky to get away with a silly moment in possession after the break, too.
Gabriel 5 - A moment of dreadful defending from the Brazilian saw Sigurdsson capitalise, though the Swansea playmaker missed an open goal. Huge let-off for the defender.
Nacho Monreal 7 - The Spaniard is arguably the most underrated left-back in the Premier League at the minute, and he was virtually flawless here again, barring one or two hairy moments against Ayew.
Francis Coquelin 5 - Okay on the whole, though his distribution could've been better, and he conceded the foul which led to Swansea's winner.
Aaron Ramsey 5 - Relatively ineffective throughout and never looked like being a threat to Swansea.
Joel Campbell 8 - You need only have heard the boos that echoed around the Emirates to get a sense of Campbell's performance. They were not for him, but for Arsene Wenger, who inexplicably substituted him with half-an-hour to go. The Costa Rican was far and away Arsenal's best player, opening the scoring and being a general menace to the visitors. His expression at being subbed said it all.
Alexis Sanchez 4 - Will the real Alexis Sanchez please stand up? Evidently not. The Chilean's confidence now looks at rock bottom. He did hit the woodwork twice, though it was simply bad finishing rather than bad luck.
Mesut Ozil 7 - The slinky German deserves better. Aside from Campbell, Ozil was the hosts' best attacking player but his team-mates could not make the most of the chances he set up.
Olivier Giroud 4 - Preferred to Danny Welbeck in attack, but the Frenchman only gave his critics more ammunition; first by spurning a very decent half chance early on, before smashing against the crossbar later in the first half from point-blank range. Anonymous second half.
Welbeck 6 - A for effort, but Welbeck never looked like being 'dat guy' tonight. Will be aggrieved over seeing Giroud start ahead of him.