A Lukas Podolski-inspired quickfire double in the second half looked to have overturned Wilfried Bony's opener but the Frenchman's calamitous late error shared the points
Wilfried Bony jumped clear of Thomas Vermaelen less than a quarter of an hour into the game, meeting Neil Taylor's cross to score against the run of play.
Despite having dominated until then, the Gunners dropped off and struggled to turn possession into meaningful attempts on Michel Vorm's goal.
The game turned on its head in the space of two second-half minutes, however, with Lukas Podolski at the heart of it. First, the substitute finished from close range before, only moments later, bursting down the left and crossing for Olivier Giroud to score.
|VIEW FROM THE EMIRATES
|By Ewan Roberts
Arsenal fans were treated to the full range of emotions on Tuesday night as despair turned to elation, only for a calamitous late own goal to rob the Gunners of all three points and ensure more misery.
Swansea took an early lead, Wilfried Bony powering a header into the back of the net, and the visitors defended resolutely until Lukas Podolski was introduced.
The German scored Arsenal's equaliser and set up what looked like the winner, only for a defensive mix-up and penalty-box pinball to result in the ball bouncing off Mathieu Flamini and rolling into an unguarded net.
Arsene Wenger thought that he had been handed the perfect response to Saturday's mauling at Chelsea but, instead, their confidence has been further dented while their grip on fourth spot looks increasingly perilous.
The result sees Arsenal two points adrift of third-placed Liverpool and six behind leaders Chelsea, while a point for Swansea will prove valuable in their fight for survival.
Kieran Gibbs and Alex Oxlade-Chamberlain both lined up for Arsenal after the Football Association cleared up the confusion that surrounded the former's sending-off in Saturday's humiliation at Chelsea.
There was no mistaking the identity of Swansea's biggest change, as Michu – responsible for two late goals in his side's 2-0 win at Arsenal last season - came into Garry Monk's starting XI for the first time in more than three months.
It was Oxlade-Chamberlain who was first to test Michel Vorm in the Swansea goal, unleashing a fierce half-volley from the edge of the box.
Swansea posed little threat in the early stages but found themselves ahead when left-back Neil Taylor, starting in place of Ben Davies, found Bony with a cross from deep, which the Ivorian headed home from 12 yards. Arsenal boss Wenger had refused to talk to the media in the build-up to Tuesday's match but it was the home fans who fell silent in the immediate aftermath of the opener.
Half of the ground mustered a cheer nine minutes later when Per Mertesacker made the net ripple with a header from a corner but his effort deceptively crept the wrong side of the left-hand upright.
Arsenal's quest for a leveller left them exposed at the back at times and Swansea wasted a chance to double their lead when they outnumbered the home defence four to two, before Santi Cazorla tested Vorm with a low strike two minutes from the break.
The hosts emerged for the second period with pre-interval boos still ringing in their ears but their chances were limited, with Tomas Rosicky's wayward 20-yard strike about as good as it got for Wenger's men.
Podolski looked bright after coming on in place of Oxlade-Chamberlain, though, and tapped home after good work by Gibbs down the right.
And the Germany attacker turned provider almost immediately after, providing the cross for Giroud to convert from close range moments later.
But Arsenal were left red-faced and despondent at the death when Leon Britton's surge into the area prompted a series of unfortunate events that led to Flamini deflecting the ball into his own net.