كتب : Omar AbdelAziz
Emmanuel Adebayor's eighth-minute penalty gave the home side an early lead, which was doubled by Cesc Fabregas ten minutes from the break.
Arsenal defender Philippe Senderos was sent off four minutes after the interval, but his dismissal had no impact on the result of the game.
Thomas Rosicky made it three on 59 minutes, but former Gunner Nwankwo Kanu pulled one back for Pompey one minute later.
Arsenal jump five spots to join Liverpool, Everton and Chelsea at the top of the table on 10 points, while Portsmouth are 11th on five.
The Gunners were off to a flying start against a Portsmouth side that have already demonstrated their toughness against the likes of Manchester United and Chelsea this term.
Robin Van Persie was brought down by David James to hand Arsenal a deserved penalty. Togo striker Adebayor sent an ice-cool penalty home for his first goal of the season.
On 35 minutes, Fabregas collected Gilberto's near-post header to notch in the Gunners' second and his second of the season from close range.
The referee decided to send off Senderos shortly after the break, when the Swiss stopper clipped Kanu on the edge of the area. The television replay showed the red card was harsh as the Nigerian was not certain to score.
However, the Gunners seemed unfazed by his expulsion as Czech playmaker Rosicky fired in the third ten minutes later with a fierce drive.
The visitors' consolation came instantly after Kanu awkwardly flicked the ball into Manuel Almunia's net, following a cross from compatriot John Utaka.