Captain Martin Odegaard struck twice inside the opening 11 minutes to put the Gunners in control on Saturday, with Bournemouth failing to register a single touch in the Arsenal box in the first half.
William Saliba netted his first goal for the club to extend that lead in the second half, while the influential Gabriel Jesus saw a strike ruled out for off-side.
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The win gives Arsenal the enviable record of being the only Premier League side so far to win their opening three matches of the season, although Manchester City can join them on nine points with victory at Newcastle United on Sunday.
Arsenal came flying out of the blocks with former City man Jesus skipping through the Bournemouth defence and teeing up Gabriel Martinelli, who was denied by Mark Travers, only for Odegaard to tap in the rebound.
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Odegaard struck again six minutes later, smashing in with his left foot to cap off another fine move that saw Jesus touch Ben White’s cutback into the Arsenal captain’s path.
The Gunners extended their advantage swiftly after the restart, with Martinelli’s deep cross knocked square by Granit Xhaka to Saliba for a curling first-time finish into the top-right corner from just inside the box.
Jesus thought he had got into the act but was denied by the VAR, shown to be narrowly offside following Odegaard’s pass, and only his goal was missing as Arsenal remained on the front foot right through to the final whistle.
Earlier Harry Kane set a Premier League record for the most goals with a single club as the Tottenham striker sealed a 1-0 win against Wolves.
Kane’s 185th top-flight goal for Tottenham Hotspur took him above Argentina striker Sergio Aguero’s total of 184 during his time at Manchester City.
It was also Kane’s 250th goal in all competitions for Tottenham, moving him 16 goals behind Jimmy Greaves as he bids to become the north London club’s all-time leading scorer.
The 29-year-old’s landmark moment came in the second half at the Tottenham Hotspur Stadium as he headed home from close-range.
Kane had scored his first goal of the season in last weekend’s 2-2 draw at Chelsea when his stoppage-time header drew him level with Aguero.
(With OPTA/Agency inputs)
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