Arsene Wenger had called for a response to the "accident" of his side's 6-0 thrashing at Stamford Bridge which ruined his 1000th match in charge on Saturday.
Having trailed to an 11th minute header from Wilfried Bony, it was not until the introduction of substitute Lukas Podolski just before the hour that Arsenal finally sparked into life with two goals in the space of 60 seconds which looked to have won the match.
First, Kieran Gibbs - whose red card at Chelsea in a case of mistaken identity was overturned on Monday night - darted down the left and supplied a low cross which was bundled home by Podolski in the 73rd minute.
The German then turned provider as he charged clear of the Swansea defence to send in a low cross which Olivier Giroud smashed past Michel Vorm at the near post.
However, Garry Monk's side - fighting to avoid being sucked into the relegation battle - had defended resolutely and were themselves dangerous on the counter-attack, eventually forcing a late equaliser. Following a disputed free-kick, the ball broke to Leon Britton at the edge of the Arsenal penalty area.
As the midfielder pressed forward, riding a couple of challenges, he stabbed the ball goalwards. It was partially blocked by Per Mertesacker, then ricocheted off goalkeeper Wojciech Szczesny and back on to Flamini before rolling into the net.
It could have been worse for Arsenal had Lee Probert not blown for full-time with Jonathan De Guzman baring down on goal - a decision that prompted an angry reaction from those in Swansea shirts.
Wenger was left less than impressed, and will be in no doubt of the challenges which now lie ahead in a campaign which has promised so much - and continues with the visit of Manchester City to the Emirates on Saturday.