Leon Balogun opened the scoring early for Steven Gerrard's Rangers before Tavares equalised less than 10 minutes later.
"Overall I'm really pleased with the performance. I think we dominated the game, we created so many chances -- I counted about eight or 10 clear chances to score -- but this game is decided in both boxes," Mikel Arteta said after the game.
"We weren't clinical in the opponent's box and we conceded two goals from two corners, which were the only chances they had apart from the counterattack from our own corner.
"It's much better from the other day and you tell that physically we were already better in the second game, the organisation was better, individually they played better, but I really liked the collective understanding of the game and how we executed a lot of things we've been working on in the training pitch."
Rangers won a corner on 14 minutes. Balogun was left unmarked in the box and hit a powerful header into the Arsenal net.
Left-back Tavares, who joined Arsenal from Benfica for around €8 million this summer, benefitted from poor play from James Tavernier to steal the ball and strike it into Allan McGregor's net on 23 minutes.
Arsenal could have taken the lead through Pierre-Emerick Aubameyang on the half hour mark but he failed to place his header on target.
Instead it was Rangers who pulled ahead in the second half when Itten scored from a header during a set piece.
However, Rangers were unable to keep Nketiah out a few minutes later when he secured the ball and struck a hard shot past McGregor to level things.