Mark Hughes started with both Robinho and Craig Bellamy, who were both doubts after injuries picked up on international duty.
City began positively and Nigel De Jong forced a save out of Manuel Almunia on five minutes with a curling 20-yard shot that the Spanish keeper secured at the second attempt.
The Gunners took the lead however on eight minutes through fit-again Adebayor. Andrey Arshavin's corner eluded Alex Song but fell to the unmarked Togolese striker, who picked his spot with a firm header.
Kolo Toure went close for the Gunners on 22 minutes after a run into the box past a couple of City players opened up the goal for the defender, but his shot was straight at keeper Shay Given.
Almunia was called upon to deny substitute Gelson Fernandes on 27 minutes after he was found by Shaun Wright-Philips, but his shot from the right side was blocked by the legs of the Gunners' keeper.
Four minutes later, the same player, again put through by the lively Wright-Philips was in on goal on the right side of the area, but his shot found the outside of the right upright.
Wright-Philips himself saw an effort dip just over the crossbar after Song half cleared a free-kick to the City attacker, who instantly sent a volley towards Almunia's goal.
Given kept his side in the game a minute before half-time when he made a fine save from Arshavin whose clever interplay with Adebayor deserved a goal.
The Gunners were 2-0 up within three minutes of the re-start after Cesc Fabregas lifted a clever pass over Richard Dunne to the feet of Adebayor, who proceeded to go around Given before rolling the ball into the net.
He came close to a hat-trick a minute later after rising to meet another Arshavin corner, but this time his header flew over the bar.
Pablo Zabaleta had a fierce 20-yard strike saved by Almunia just before the hour, but that was the extent of their threat.
Theo Walcott had a screamer saved by Given on 68 minutes just before being replaced by Emmanuel Eboue, then Aaron Ramsey had an effort comfortably saved by Given in the dying minutes.
That was the extent of the noteworthy action as full-time approached and the Gunners passed the ball around, training ground style, clearly with one eye on Villarreal this coming Tuesday.