The Citizens went into the half-time break with a slender lead after Sergio Aguero had broken the deadlock on the half-hour mark.
However, the Gunners fought back strongly after the half-time break as goals from Alex Iwobi, Theo Walcott and Chuba Akpom fired the London outfit into a two-goal lead.
Nigeria international Kelechi Iheanacho reduced the deficit two minutes from time, but it was a case of too little, too late as Arsenal held on for the win.
Earlier, Liverpool were brought crashing back down to earth following their 4-0 win over Barcelona as Jurgen Klopp's former side Mainz inflicted the same score on the Reds.
Daniel Brosinski handed Mainz the lead from the penalty spot in the 15th minute, before Jhon Cordoba doubled their advantage on the stroke of half-time. Yunus Malli notched Mainz's third after the interval, while Yoshinori Muto rubbed further salt in the wounds of the Reds with Mainz's fourth on 74 minutes.
Antonio Conte's Chelsea were also in action and produced a strong team performance as they clinched a 4-2 victory over Bundesliga outfit Werder Bremen at Weserstadion.
The Blues raced into a two-goal lead early on, Eden Hazard and Oscar both getting on the scoresheet inside the opening ten minutes of play.
Claudio Pizarro pulled one back from the penalty spot in the 32nd minute, only for Diego Costa to restore Chelsea's two-goal cushion just moments before the half-time whistle.
Lennart Thy gave the hosts a way back into the contest when he slotted home after the half-time break to make it 3-2, but Pedro Popped up in the 90th minute to put the result beyond doubt.