Theo Walcott got the scoring out of the way early as he struck home a low cross from Aaron Ramsey.
The hosts managed to maintain the lead throughout the first half despite reasonably even possession and a number of chances for both sides.
The striker seemed likely to bookend the match with goals as he struck from a cross from Gervinho on the cusp of full time. However, a save from Samir Handanovic left the Gunners with just a one-goal advantage.
Arsenal will visit Italy for the second leg of the qualifier on Wednesday, August 24.