The Gunners' comfortable win was aided by the sweeping changes made by Pompey manager Harry Redknapp, who clearly had Saturday's game against fellow relegation candidates Fulham on his mind.
Dennis Bergkamp opened the scoring in the seventh minutes after Mathieu Flamini threaded a perfect ball for Jose Antonio Reyes to run onto on the left flank. The Spaniard cut in before crossing for Bergkamp to slide in and guide the ball past Jamie Ashdown from eight yards out.
Arsenal's second came just six minutes later when Kolo Toure hit a perfectly weighted pass to the right side of the Portsmouth area for Thierry Henry. The Frenchman checked back to put Andy O'Brien on his backside before rolling the ball to Reyes to shoot hard into the roof of the Portsmouth goal.
The hosts then began to play with real confidence and despite their efforts the visitors spent much of the time chasing shadows. With the busy schedule in their thoughts the Gunners looked to be conserving energy.
They burst into life in the 37th minute with Flamini again instrumental, when he delivered an angled pass for Henry to latch onto. The skipper surged into the area and beat a defender before rounding Ashdown and firing into the net from an acute angle.
Henry moved within three of Cliff Bastin's league goals record with a cheeky penalty on 43 minutes.
Andy Griffin had hacked down Reyes as the Spaniard looked to turn in Robert Pires' ball. The referee had no hesitation and awarded a penalty but spared Griffin a caution.
Henry, who has already missed two penalties this season, walked up to the ball and clipped it towards the right side of the goal as Ashdown dived the wrong way.
Portsmouth showed more endeavour after the break. Their best opportunity came after 55 minutes, when Lomana LuaLua worked a chance on the left and his looping shot beat Jens Lehmann but cannoned back off the bar to safety.
Matthew Taylor tested Lehmann a minute later, but the German keeper coped comfortably with the 20-yard effort.
At the other end Bergkamp brought a fine save from Ashdown and Henry also shot just over, but that was the sum of Arsenal's threat in the second half.