Arsenal boss Arsene Wenger endured, rather than celebrated, his 1,000th game in charge as his side lost 6-0 at Chelsea on Saturday.
And things did not get much better as the tally ticked to 1,001 at the Emirates Stadium on Tuesday.
Wilfried Bony put the visitors in front with an early header, but substitute Lukas Podolski converted from close range in the 73rd minute, before providing the assist for Olivier Giroud just over one minute later.
The defining moment came in second-half stoppage time though, when the ball rebounded into the Arsenal net off Flamini after hitting the feet of goalkeeper Wojciech Szczesny.
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 Stamford Bridge humiliation.
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 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.
