Goals from Gylfi Sigurdsson and Bafetimbi Gomis undid the strike from Alexis Sanchez.
In the torrential rain at The Liberty Stadium they struggled to get a foothold on proceedings and were rightly beaten despite taking a 1-0 lead.
The man who gave them the lead was Alexis Sanchez. The Chilean forward scored once again, continuing his fine form in front of goal for The Gunners. Danny Welbeck raced clear down the right hand side before cutting back and laying the ball on a plate for Alexis to strike.
The goal was of course scored past former Arsenal goalkeeper Lukasz Fabianski. He was not the only ex-Gunner to start the game. Kyle Bartley played at centre-back in the absence of Federico Fernandez and Jordi Amat.
Soon enough Swansea were back in the game. Former Tottenham midfielder Gylfi Sigurdsson was the hero. Well known for his abilities from free-kicks, he lined up a strike from 25 yards. He hit the ball beautifully, leaving Wojciech Szczesny with no chance.
The game was clearly slipping away from Arsenal. The performance of Calum Chambers in particular was not pretty viewing. The Englishman struggled to deal with the pace of Jefferson Montero for the majority of the game, and this eventually lead to the winning goal.
Just moments after coming on as a substitute French striker Bafetimbi Gomis headed home what proved to be a winning goal as Arsenal's title hopes simply fade away.