The Gunner bounced back from their disappointing 0-0 draw with Sunderland last weekend with a win over the Canaries.
Ozil was unable to add to his Premier League assists tally which stats at 18.
The 27-year-old played the full 90 minutes and received a yellow card in the 85th minute. Arsenal moved up to third place following their win over the relegation battlers.
However, Manchester City can overtake the Gunners if they win their game in hand against Southampton this weekend. Arsenal take on Man City next weekend in the Premier League.
Arsenal 1 – 0 Norwich
Kick-Off: 17:30 (GMT)
Stadium: Emirates Stadium
Arsenal: Cech; Bellerin, Mertesacker, Koscielny, Monreal; Ramsey, Elneny; Sanchez, Ozil, Iwobi; Giroud
Norwich: Ruddy; Pinto, Martin, Bassong, Olsson; Brady, Howson, O’Neill, Redmond; Hoolahan; Jerome