- Sanchez scores sixth goal in his last four league games
- Arsenal lose their second league match this season
- Gylfi Sigurdsson scores his second goal of the campaign
- Swansea have claimed 13 points from 18 at home
Swansea came from behind with two late goals to claim a memorable win over Arsenal at the Liberty Stadium
Arsenal took the lead when Alexis Sanchez finished from close range after an excellent run and pass from Danny Welbeck.
But a stunning Gylfi Sigurdsson free-kick and a fine header from substitute Bafetimbi Gomis sealed Swansea's victory.
The win sees Garry Monk's men leapfrog the Gunners into fifth place in the Premier League table.
For Arsene Wenger's side, meanwhile, defeat caps a miserable week after their Champions League collapse against Anderlecht on Tuesday, in which they threw away a three-goal lead to draw 3-3.
There were some nervy moments from the Gunners' defenders, with Calum Chambers surviving a Swansea penalty appeal after appearing to shove Wilfried Bony to the ground inside the area.
Clear scoring opportunities were at a premium in the first half as two slick but congested midfields cancelled each other out.
Arsenal did not manage a shot on target until a minute before half time, as Welbeck combined well with Sanchez before his effort was palmed away by former Gunner Lukasz Fabianski.
Arsenal's flashes of danger before the break were a sign of things to come, as they made the stronger start to the second half.
Alex Oxlade-Chamberlain wasted an excellent opportunity when his shot was saved by Fabianski, but the Gunners were ruthless with their next effort.
The visitors latched on to a poor pass from Bony and launched a counter-attack, from which Welbeck sped into the box, turned past Ashley Williams and squared the ball for Sanchez, who fired in from six yards.
Arsenal seemed in control at this point but, within 15 minutes, the match was completely transformed.
Swansea were awarded a free-kick 25 yards from goal after Kieran Gibbs was booked for fouling the hosts' debutant Modou Barrow.
Sigurdsson then compounded Gibbs' punishment as he curled an unstoppable shot into the top corner.
Arsenal barely had time to register the blow of Sigurdsson's leveller by the time Swansea took the lead less than three minutes later.
Montero, who had given Chambers a torrid afternoon on Swansea's left wing, floated in an inviting cross for Gomis, who nodded the ball beyond a static Szczesny and into the bottom corner.
Arsenal tried to salvage a point with some desperate long balls late on, but Swansea withstood the pressure to claim a first win in six games against the Gunners.
Swansea manager Garry Monk: "It's about belief. We talked about belief before the game, about how good we have been and how good we can be. We showed our character.
"They got the goal. I thought it was an even game, we made the changes and thankfully they went for us today.
"Gylfi Sigurdsson has been disappointed previously that he has not had many opportunities to produce what he did today but what a great goal and that put us in the ascendency.
"We beat Manchester United on the first day, we have just beaten Arsenal but we take each game as it comes. We are doing a lot of work on the training ground and at the moment it is paying off."
Arsenal manager Arsene Wenger: "It's disappointing to throw a game away like we did. We were 1-0 up and had to be tight defensively and wait for that second chance. But you have to credit Swansea who didn't give up.
"In football you can believe anything is possible, any minute you can concede. Bafetimbi Gomis is good in the air and it can happen. You have to accept that Swansea will fight until the last minute. We eased off at 1-0 and let them back into the game.
"Football is down to performances. We are here to produce performances, and didn't do that right until the end of the game."
