A scrappy start to the final after the corresponding pre-match ceremonies saw Arsenal settle first on the ball. With Conte's men unable to claim possession, the Gunners looked more intense in the opening minutes.
And Sanchez put the ball into the back of the net, only for the referee to stop the game for a moment of confusion. The Chilean had scooped the ball behind the defence, with Ramsey in an offside position interfering in the play despite not getting a touch. Sanchez himself ran onto it and powered the ball past Courtois, after what looked like a handball from the striker.
The goal was finally given after the official spoke to his assistant, with the Arsenal end going ballistic and the Chelsea players furiously appealing for the handball.
Following the initial controversy, Arsenal continued to look best as they knocked the ball around well, while Chelsea looked shell-shocked having gone behind so early.
The Blues appeared to respond when Costa's shot inside the penalty area was blocked, but the Gunners were straight up the other end. Ozil scuffed his finish over Courtois, and the ball was heading in for a second before Cahill got back to back-heel the ball off the line.
More clear chances came Arsenal's way as they were unfortunate to hit the post twice in quick succession. Welbeck headed Ozil's corner onto the back post, and the ball rebounded onto Ramsey and back off the post.
Arsenal dominated the first thirty minutes with some of the best minutes they have offered all season, and they had chances to go two or three up.
Chelsea's efforts were few and far apart, with their best opportunity in a frenetic first half coming when Pedro blazed his strike from inside the box just over the bar.
The Gunners were in front as the teams headed for the changing rooms at half time, after Premier League champions Chelsea were second-best in the affair having been swamped by Wenger's team.
The Blues came out better in the second period, and Moses fired the first warning, forcing a good save from Ospina from the wing-back's low drive, but they still looked unusually susceptible in defence, as Arsenal breached their lines without difficulty.
Courtois saved his side at one end when Bellerin side-footed the ball towards the bottom corner, and Chelsea were at the other end soon after with Moses going down in the box. The official blew his whistle leading the Chelsea players to believe a penalty had been given, but the second yellow card came out for Moses, as he was sent off for simulation.
From then on, Arsenal's title hopes increased drastically, the win theirs to throw away. And it looked that way when Costa brought down Willian's cross with his chest and volleyed towards goal. His finish took a slight deflection before beating Ospina at the near post.
Wenger reacted by bringing on Giroud for Welbeck, and the impact was instant as the Frenchman pulled the ball back from the byline for Ramsey to head easily into the net, about a minute after Chelsea's leveller.
Chelsea continued to push forward, and Arsenal did nothing to kill the match, which still ricocheted uncontrollably from one end to the other.
Arsenal almost managed to put the game out of reach for the Blues, with Ozil rattling the post having cut onto his left foot inside the area.
In the end, they held off the Premier League champions after four minutes of stoppage time. The Gunners came out on top in one of the best FA Cup finals in recent times, to deny Conte a double and for Wenger to become the only manager to win seven FA Cups.