Aaron Ramsey scored the winner for Arsenal
Victory for the Gunners sees Arsenal go one ahead of Manchester United's 12 FA Cup triumphs.
A thrilling encounter at Wembley had everything – drama, goals and a sending off – as Wenger secured his seventh FA Cup win.
Many had written Arsenal off before the game had even started due to their injury woes at the back against an attacking Chelsea side that had won the Premier League title only a few weeks ago.
But Arsenal were fearless throughout and Alexis Sanchez fired Arsene Wenger's side ahead after just four minutes – although it was somewhat controversial.
Sanchez's goal was initially ruled out as Aaron Ramsey was caught in an offside position but the decision was overruled by referee Anthony Taylor – despite replays showing the ball striking the Chilean's hand.
Alexis Sanchez handball controversy for Arsenal against Chelsea Sat, May 27, 2017
Alexis Sanchez was involved in a hugely controversial moment during the FA Cup final
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Arsenal lift the FA Cup after beating Chelsea 2-1 at Wembley Chelsea player ratings against Arsenal in the FA Cup final Sat, May 27, 2017
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Thibaut Courtois – 6
In the second half Victor Moses was sent off on 68 minutes after a silly dive in the box that gave Arsenal a crucial advantage.
However, Chelsea equalised just eight minutes later through Diego Costa when Arsenal keeper David Ospina failed to keep out his deflected shot
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Arsenal hit straight back though as Aaron Ramsey popped up with the winner late on.
Ramsey, who scored the FA Cup final winner against Hull City in 2014, headed home from Olivier Giroud's cross to give Arsenal fans something to smile about in what's been a frustrating season.