Idrissa Gueye stole possession from Granit Xhaka to allow Wayne Rooney to break, and the former Manchester United and England captain curled in a superb 20-yard strike almost 15 years to the day he scored a similar effort on this turf against the same opponents.
Jordan Pickford kept Arsenal at bay for long stretches of the first half, but could only parry a low shot into the path of Nacho Monreal to expertly volley home Arsenal's deserved equaliser five minutes before the interval.
Ronald Koeman's hosts could not cope with the movement of Arsenal's front trio of Alexandre Lacazette, Alexis Sanchez and Ozil, and it was the latter duo who combined to put the visitors in front.
Sanchez dropped out wide on the left before curling an inviting cross into the six-yard area, which Ozil flicked past Pickford after 53 minutes.
Things got worse for Everton as Gueye was given his marching orders for a second bookable offence following a late challenge on Xhaka with 22 minutes left on the clock, and Ozil then teed up Lacazette to bury Arsenal's third six minutes later.
There were time for more goals late on as Jack Wilshere teed up Aaron Ramsey to finish the fourth for Arsenal, while Cech was left embarrassed as Oumar Niasse stole the ball off the goalkeeper for an injury-time consolation effort - but Sanchez netted in the 95th minute to restore the visitors' three-goal advantage.
The result sees Arsenal up to fifth in the table and nine points behind league leaders Manchester City, while Everton slip into the bottom three with Koeman's position now in severe doubt. THINK YOUR FRIEND WOULD BE INTRESTED? SHARE THIS STORY USING ANY OF THE SHARE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>