The 27-year-old provided the assist of the Gunners opening goal in the 36th minute.
Arsenal went onto double their lead two minutes later when Koscielny headed in from Santi Cazorla’s free-kick.
Özil now has a total of seven assists in all competitions for the north London based club this season.
Arsenal v Everton
Kick-Off: 17:00 GMT
Arsenal confirmed starting lineup: Cech; Bellerin, Gabriel, Koscielny, Monreal; Coquelin, Chamberlain; Cazorla, Ozil, Sanchez; Giroud
Subs: Macey, Debuchy, Gibbs, Chambers, Flamini, Campbell, Walcott
Everton confirmed starting lineup: Howard, Coleman, Galloway, Jagielka, Stones, Barry, McCarthy, Lennon, Deulofeu, Barkley, Lukaku.a
Subs: Joel, Kone, Mirallas, Naismith, Cleverley, Osman, Funes Mori