Arsenal dominated the first half and went into the interval with a 1-0 lead thanks to Olivier Giroud's early strike, but Craig Gardner equalised from the penalty spot in the 48th minute.
Aaron Ramsey sealed victory for the Gunners with two goals but, between his fine strikes, there was a moment of bad luck for Sunderland when referee Martin Atkinson pulled the game back for a free-kick for a foul by Bacary Sagna on Jozy Altidore, even though the American striker managed to shrug off the challenge and put the ball in the net.
Wenger was satisfied with the efforts of his side, telling Sky Sports: "There were plenty of chances on both sides. We had a great first half and maybe it should be game over at half-time, but Sunderland came back with a great determination.
"We dropped a bit physically but at 1-1 we found the resources again."
Asked if Arsenal had been lucky, Wenger said: "A little bit, yes. I think he blew early."
Wenger paid tribute to the improved finishing of Ramsey and also hailed Ozil's performance on his first start for Arsenal after signing from Real Madrid.
The German was particularly influential in the first half as he set up Giroud's goal and created a number of other good chances.
Wenger said: "It was especially good because he was sick yesterday. His first half was outstanding, in the second half he dropped a bit physically but overall it was good."
The most disappointing part of the afternoon for Arsenal was seeing Giroud go off near the final whistle with an injury that will have to be assessed.
Wenger admitted: "We are on a very strong run, but we are a bit short because we have so many injured players and every player we lose makes it difficult."