The Germany international's future has been called into question in recent weeks, with the attacking midfielder struggling for game time under Unai Emery.
However, the 30-year-old was back to his brilliant best against Sean Dyche's side.
Ozil wore the captain's armband during the game, which Arsenal won 3-1, and produced a phenomenal pass in the build-up to Pierre-Emerick Aubameyang's opening goal.
Following the match, Ozil wrote on Twitter: "YaGunnersYa (sic). Very valuable 3 points won. Glad I could help the team today!"
The Germany international has been heavily linked with a January loan move away from the Gunners, as the club looks to get his £350,000-per-week wages off of their bill.
"Mesut Ozil is a precious player," Gumusdag said, as quoted by Bild .
"I hope one day our paths will cross at Basaksehir.
"If he wants to be with us as well, we would do anything to get him."
Ozil has scored four goals and provided three assists thus far this season, while Arsenal currently lie fifth in the Premier League table.