Everton slipped into the relegation zone after a 5-2 drubbling at the hands of Arsenal at Goodison Park on Sunday.
Arsenal started superbly but after failing to make the most of a number of good chances, it was none other than Wayne Rooney who would open the scoring.
The goal came after the pedestrian Granit Xhaka was robbed in midfield, before Rooney produced a fine curling long-range strike which recalled his famous goal against the Gunners in 2002.
The visitors pushed for a leveler, with Jordan Pickford keeping his side ahead.
However, before the break, the Gunners finally scored, with Nacho Monreal netting after Pickford had parried a Xhaka shot.
After the break, the superb Ozil put Arsenal ahead, heading home from a deft Alexis Sanchez cross.
Things got even worse for Ronald Koeman when, on 68 minutes, Idrissa Gueye picked up a second yellow after a needless challenge on Xhaka.
The north Londoners were now cruising, and on 74 minutes, Alexandre Lacazette got on the scoresheet to make it 3-1, from an Ozil assist.
Late on, Aaron Ramsey got the goal his good performance deserved.
There was time, however, for Arsenal to conjure up a trademark defensive blunder, with sub Oumar Niasse capitalising on a mix-up between Monreal and Petr Cech.
With Goodison Park starting to empty, Alexis Sanchez netted a superb individual goal to seal an impressive victory for the Gunners.
The result increases the pressure on Koeman, who is yet to see his summer-signings blend into a competitive side capable of building on last season’s seventh-place finish.
As for Arsene Wenger, he celebrated his 68th birthday with an impressive win which saw Ozil, Sanchez and Lacazette link up superbly throughout the game.
Everton are now 18th, with Koeman’s future at Goodison anything but certain, while the Gunners move up to fifth, level on points with Chelsea.