Eduardo, Samir Nasri, Aaron Ramsey and Alex Song's first of the season were enough for the Gunners to breeze past Pompey, who claimed a late consolation through Nadir Belhadj.
Portsmouth had two early opportunities as first Richard Hughes scuffed a volley on the edge of the penalty area following some good work from Frederic Piquionne.
Kevin-Prince Boateng then stole the ball off Song on the halfway line before progressing forward but failed to trouble Manuel Almunia.
After that early blip Arsenal dominated the remainder of the half and gave Portsmouth an early indication of their might when Andrey Arshavin fed Bacary Sagna but the France full-back's cross was just too high for Eduardo.
Pompey goalkeeper Asmir Begovic then denied Abou Diaby at his neat post after Eduardo had found space on the byline to free the lanky midfielder.
The opener for the visitors was inevitable but it arrived in almost un-Arsenal like circumstances as Aaron Mokoena's crude lunge on Ramsey brought up a free-kick 25 yards out.
Eduardo fired low towards Begovic's far post only for the ball to strike Younes Kaboul and roll past Hermann Hreidarsson waiting on the goalline.
Belhadj tried to hit back in anger with a skidding left-footed strike but it proved to be a brief revival as Arsenal doubled their lead three minutes before the break.
Eduardo shaped to shoot but instead passed to Ramsey, who helped the ball onto Nasri for the young French midfielder to find the corner and give Arsenal a dominant lead.
After the break Pompey tried to rally but were three down when the excellent Ramsey tackled substitute Anthony Vanden Borre before firing a stunning drive into the corner of the net.
The home side were not to be completely embarrassed as they gave their suffering fans a temporary glow with Belhadj and Vanden Borre exchanging passes before the Algerian fired past Almunia.
Arsenal still had time for a fourth as Nasri had all the time in the world to pick out Song at the far post and the Cameroon midfielder promptly headed past Begovic.