The Swans claimed a famous victory at The Emirates Stadium as Michu scored twice late on to send Michael Laudrup's side up to seventh in the Barclays Premier League table.
In a memorable day for the club, the Swans were deserved victors as Michu fired home in the 88th minute to put the visitors ahead before he scored his tenth league goal in added on time to seal the victory.
His first came after a delightful first-touch pass from sub Luke Moore, who sent the midfielder in on goal before he fired past Wojciech Szczesny and into the far corner as the game looked to be edging to a draw.
His second came in added on time, superb persistence from Nathan Dyer saw the winger take possession off Carl Jenkinson on the halfway line with Michu latching onto the loose and calmly picking his spot to beat Szczesny.
This win continues the Swans' fine run of form - now beaten just once in the last ten games - which includes victories on the road at Liverpool in the Capital One Cup and Newcastle.
Laudrup made two changes, with Pablo Hernandez and Wayne Routledge missing through injuries.
That meant Jonathan de Guzman started on the left wing while Itay Shechter was recalled to the starting XI as he fulfilled the lone striker role with Michu dropping back into midfield.
Arsenal: Wojciech Szczesny, Per Mertesacker, Thomas Vermaelen, Mike Arteta, Lukas Podolski (Olivier Giroud, 68), Jack Wilshere (Tomas Rosicky, 81), Gervinho (Alex Oxlade-Chamberlain, 68), Theo Walcott, Santi Cazorla, Cark Jenkinson, Marouane Chamakh.
Subs: Vito Mannone, Aaron Ramsey, Sebastien Squillaci, Francis Coquelin.
Swans: Gerhard Tremmel, Angel Rangel, Chico Flores, Ashley Williams (capt), Ben Davies, Leon Britton, Ki Sung-Yueng, Michu, Jonathan de Guzman (Dwight Tiendalli, 76), Nathan Dyer, Itay Shechter (Luke Moore, 68).
Subs: David Cornell, Garry Monk, Kemy Agustien, Jazz Richards, Rory Donnelly.
The Swans settled early into the contest, with Michu almost finding Itay Shechter with a through ball while Ashley Williams failed to connect properly with a loose ball after Jonathan de Guzman got onto the end of Jack Wilshere's headed clearance before seeing his shot deflect into the patch of the Wales skipper.
Then the visitors went even closer, Angel Rangel being denied twice by Wojciech Szczesny after Itay Shechter slipped in the Spaniard, who was left unmarked just inside the Arsenal box.
Arsenal replied when Santi Cazorla headed straight at Gerhard Tremmel from Carl Jenkinson's cross, before the Swans carved open the best chance of the game so far. Michu flicked on Rangel's pass and Nathan Dyer out-paced the defence to race in on goal, but Thomas Vermaelen covered back in time to deflect his effort over the crossbar for a corner.
Jonathan de Guzman then fired a 20-yard free-kick which dropped onto the netting and over the crossbar, before the Swans went into the break level after an encouraging first half.
Half-time: Arsenal 0 Swans 0
Arsenal made a bright start to the half, Cazorla firing straight at Tremmel after being teed up by Jack Wilshere, and then Shechter saw his effort deflected for a corner after a fine through pass from Rangel.
Cazorla then tried his kick from 20 yards, which took a touch off Lukas Podolski, but Tremmel gathered well.
The Swans replied via Rangel, who cut inside and beat Vermaelen before firing a powerful right-footed shot to the near post but Szczesny swatted it away for a corner.
With the game past the hour mark, Arsene Wenger made a double change with Alex Oxlade-Chamberlain and Olivier Giroud replacing Gervinho and Podolski.
Laudrup also made a change, Luke Moore on for Shechter in a straight swap up front.
Arsenal then saw a penalty appeal turned down as Giroud went down under a challenge from Chico Flores, but Mark Clattenburg waved down the appeals.
The hosts were raising the pressure, and Cazorla was again probing as his volley was neatly collected by Tremmel.
Moore then sent a through ball for Michu to run onto, but the Spaniard's effort failed to trouble Szczesny from an acute angle.
Laudrup then made another change as Dwight Tiendalli replaced de Guzman, which saw the Dutch defender come on at right-back, with Rangel pushing forward and Dyer switching flanks to the left.
Wenger made his final change for the last ten minutes as Tomas Rosicky replaced Wilshere.
But it was a Swans sub that made the next big impact as Tiendalli lost Oxlade-Chamberlain and raced into the box after a one-two with Moore. But the Dutchman was denied by a terrific save by Szczesny.
Tremmel then collected Vermaelen's header from Oxlade-Chamberlain's cross as the game ticked into the last two minutes of normal time.
Then came the big moment, Chico's pass finding Michu, whose touch deflected off Vermaelen to Moore and his excellently-judged first-time pass sent in Michu, who fired into the far corner with a powerful left-footed effort which gave Szczesny no chance.
It looked like the Swans would have to dig deep to hold on, but it didn't prove the case.
When Dyer put Jenkinson under immense pressure, the winger slid in to dispossess the full-back with the ball falling to Michu. The Spaniard raced on and coolly slotted past Szczesny in added on time to put the icing on the cake.