Alexis scored in the first half to give the Gunners the edge, but they were unable to score even a point as they conceded very late on.
Ashley Williams proved to be the unlikely hero for 10-man Everton as they handed Arsenal their second Premier League defeat of the season by securing a dramatic 2-1 victory at Goodison Park on Tuesday.
Defender Williams headed home Ross Barkley’s corner in the 86th minute to clinch just a second league victory in the last 11 outings for Ronald Koeman’s side
Alexis Sanchez’s 12th league goal of the season had given the visitors a 20th-minute lead, though his free-kick needed a deflection off the unfortunate Williams to find the net.
Yet any ideas Arsene Wenger’s men had of taking over from Chelsea at the top of the league disappeared when they conceded late on in each half to lose on their travels for the first time since March.
Everton levelled just prior to the interval when full-backs Leighton Baines and Seamus Coleman conjured up an equaliser, the former’s right-footed cross setting up the latter to head home from close range.
Williams then popped up with a winner, although that was not the end of the drama. Phil Jagielka saw red in injury time after picking up a second booking, as the hosts just about held firm in a frantic finish.
Barkley, in as one of four changes from the defeat at Watford, was involved in the opening goal too, surrendering possession to trigger an Arsenal counter-attack that was emphatically halted by Phil Jagielka’s lunge on Francis Coquelin.
Sanchez capitalised on the set-piece opportunity, his low strike from the edge of the area clipped off Williams’ standing leg and beyond wrong-footed goalkeeper Maarten Stekelenburg.
But, after a tepid start, Everton eventually warmed to their task.
Romelu Lukaku and Aaron Lennon both wasted opportunities to test Petr Cech by blasting wide before Coleman scored a deserved equaliser a minute before the break.
Having gambled on running into the penalty area from his usual position on the flank, Coleman was picked out by an inviting centre from Baines to nod his side level.
Arsenal wasted a glorious chance to retake the lead in the opening minutes of the second half when Mesut Ozil lifted his shot over after meeting Sanchez’s low cross from the left.
The German looked set to have another opportunity as Hector Bellerin’s pass put him through on goal, only for Stekelenburg to rush from his line and smother the danger.
At the other end, Cech was relieved to see Barkley drag a low, left-footed drive just wide of the target.
Wenger summoned Alex Iwobi and Olivier Giroud from the bench in an attempt to find a winning goal in the final 20 minutes, yet it was Williams who had the final say with his first Everton goal.
The Wales international rose high to powerfully head home, then showed strength in his own penalty area during a goalmouth scramble in injury time after Jagileka had been dismissed by referee Mark Clattenburg.