Arsene Wenger made four changes from the team that conquered Everton and came away from Glasgow with a 2-0 over Celtic earlier in the week.
Emmanuel Eboue came in to his preferred right-back spot in favour of the Bacary Sagna, who was on the bench along with Gael Clichy, Alex Song and Nicklas Bendtner.
Eduardo started up front alongside Robin Van Persie with Abou Diaby in for Song and Kieran Gibbs for Clichy.
Diaby made his opportunity count by scoring two goals in the first 22 minutes. He put the Gunners ahead on 19 minutes when he fired home from a central position on the edge of the area after Eduardo skinned the Pompey right-back to tee the Frenchman up with a pass back from the by-line.
His second came three minutes later from slightly nearer to goal. This time it was Eboue who supplied the pull-back for Diaby to sidefoot powerfully past David James.
Arsenal pinned Pompey back for virtually the whole of the first half and James kept the deficit down with some fine saves, particularly from Van Persie.
Portsmouth halved the arrears on 36 minutes when a Niko Kranjcar corner from the right found its way to Nadir Belhadj on the left. He floated in a cross which Younes Kabul got to before Manuel Almunia and nodded home from a little over a yard out.
Arsenal lost their talisman Cesc Fabregas at half-time. That may have spurred on Portsmouth, who came close when Frederic Piquionne opened up the Gunners on the right side.
The Pompey striker failed to keep his composure and fired into the sidenetting from close range.
The Gunners went further ahead in the 51st minute with another bizarre goal from William Gallas. A cross from Van Persie was headed goalwards by Thomas Vermaelen into the path of Gallas, who sliced a shot onto his own head before it bounced past James.
The Gunners made it 4-1 on 68 minutes when Aaron Ramsey ran into the Pompey penalty area to meet a defence-splitting pass from Van Persie.
The youngster, on for Fabregas, coolly fired into the bottom left corner past the visitors keeper. James was replaced shortly afterwards by Asmir Begovic.
Portsmouth offered little but managed to restrict the Gunners to four goals, which in itself was something given the goal-scoring form that Wenger's side have hit already this season.