Goals from Carlos Vela, Bacary Sagna and Samir Nasri were enough for the English Premier League side to beat their Scottish counterparts, who replied through Daryl Murphy and Ki Sung-yueng.
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Victory put Arsenal top of the table on eight points with France's Lyon and Celtic on five and Serie A side AC Milan on four.
The annual pre-season tournament, held at Arsenal's Emirates Stadium, awards one point for each goal scored as well as three for a win and one for a draw.
Arsenal forward Vela poked home after just three minutes and the hosts doubled their lead on the stroke of halftime through Sagna's powerful low drive from outside the area.
Slack defending allowed French midfielder Nasri to stroke in a third after 51 minutes, before Celtic threatened a comeback.
Greece striker Georgios Samaras missed a penalty and then Murphy and Sung-yueng netted late on.
Earlier, Milan and Lyon played out an entertaining 1-1 draw. The Italian club took an early lead through Marco Borriello only for Lyon's new signing Jimmy Briand to equalise with a far post header after the break.
On Saturday, last season's Ligue 1 runners-up, Lyon, had looked on course for victory against Celtic after goals from Michel Bastos and Harry Novillo, but the Scottish side hit back with late strikes from new frontman Gary Hooper and Samaras.
In Saturday's other match, new signing Marouane Chamakh announced himself to the Arsenal fans with his first goal on 36 minutes against AC Milan. The Londoners were pegged back by Brazilian striker Alexandre Pato 13 minutes from time.
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