Thierry Henry scored a hat-trick to inspire Arsenal to victory.
The Frenchman collected Lauren's cross and tucked away a low shot on 39 minutes for his first and then slotted in a neat finish after the break.
Pompey keeper Kostas Chalkias was at fault for Henry's third, spilling the striker's curling free-kick.
Portsmouth's best chance fell to Yakubu, who outjumped Pascal Cygan but saw his header crash back off the bar in the first half.
It was not the only time that Portsmouth's aerial threat - along with the pace of Lomana LuaLua - caused Arsenal problems.
Pompey skipper Arjan de Zeeuw also took advantage of hesitancy in the Gunners defence but directed his header wide.
And LuaLua enjoyed success down the right-hand side first against Kolo Toure and then against Lauren.
Toure had begun at right-back but moved into the middle of defence after Cygan limped off injured.
Arsenal had posed more of a threat in the early stages as 18-year-old Quincy Owusu-Abeyie - making his Premiership debut - linked well with Henry.
But, for all their possession, Arsenal failed to carve out any clear-cut chances.
And Yakubu was unlucky not to open the scoring when he exposed Arsenal's inability to deal with high balls into the box.
But just before half-time, substitute Lauren made a forceful run down the right and picked out Henry, who notched his 20th Premiership goal of the season.
Patrick Vieira should have doubled the advantage when for once a goalkeeping error was not committed by Arsenal's man between the posts.
Chalkias dropped Henry's corner at the Gunners skipper's feet but the Frenchman blasted over the bar.
Portsmouth's resistance was less stubborn after the break - particularly down their left-hand side as Arsenal stepped up the pace.
Cesc Fabregas - the smallest man on the pitch - had a headed chance after a cross from the right.
But Arsenal's second goal was fashioned through the middle of the pitch.
Vieira played a perfectly weighted pass to Henry, who showed composure to finish neatly.
Portsmouth showed their fighting qualities and pressed for a way back into the game.
Steve Stone tested Jens Lehmann with a stinging shot and Yakubu was inches wide with a low shot after good work from LuaLua.
But the last word went to Henry, who curled in a free-kick - which Chalkias should have done better with - to complete his hat-trick.
Arsenal boss Arsene Wenger:
"I feel we showed, with a very young team, that we are solid, mentally strong and efficient.
"We always looked dangerous and we needed to show patience as they packed the midfield - as many teams do here.
"We showed a lot of maturity, great discipline and real Arsenal spirit. We never gave anything away and we won in a comfortable way."
Portsmouth coach Joe Jordan:
"We started reasonably well and had one or two opportunities prior to their first goal but you have to keep concentration for the full 90 minutes.
"It became more difficult after the second goal and they exploited us.
"We didn't deserve anything from the game. You like to think you can come here and give a performance that merits something, but it didn't."
Arsenal: Lehmann, Toure, Cygan (Lauren 24), Senderos, Cole, Fabregas (Ljungberg 78), Vieira, Flamini, Clichy, Henry, Owusu-Abeyie (Van Persie 74). Subs Not Used: Almunia, Eboue.
Goals: Henry 39, 53, 85.
Portsmouth: Chalkias, Griffin (Primus 26), Stefanovic, De Zeeuw, Taylor, O'Neil, Stone, Skopelitis, Berger (Kamara 70), LuaLua, Yakubu. Subs Not Used: Hislop, Fuller, Mezague.
Booked: Primus, Stefanovic.
Ref: C Foy (Merseyside).