The sides were drawing 1-1 at the midway point at AFG Arena on Thursday after Mirlind Kryeziu converted a penalty to cancel out debutant Marquinhos’ 16th-minute opener.
It was decided that a period of reflection would be held ahead of the second half, with Arsenal playing the remainder of the Group A contest with black armbands.
Eddie Nketiah – heavily involved at both ends – put Arsenal back ahead after the hour mark in Switzerland and the visitors saw out their sixth win in seven matches this season.
Zurich are winless in seven league matches in what has been a poor start to the season and were behind early on against Arsenal.
Nketiah carried the ball down the left and picked out Marquinhos, who thumped an impressive first-time finish into the roof of the net.
Having played a big part in that opener, Nketiah went from hero to zero when bringing down Fidan Aliti to concede a penalty, which Kryeziu slotted in to level up the contest.
After a sombre start to the second period, Arsenal soon got going and regained their lead through an Nketiah header – Marquinhos turning provider with his cross from the right.
Arsenal were unable to find a third goal, but they held their opponents firmly at bay to respond to Sunday’s loss against Manchester United in the best way possible.