Denmark international Bendtner opened the scoring after his header was fumbled over the line by Portsmouth goalkeeper David James before adding a second from the penalty spot.
With Pompey stretched and forced to chase the game, Arsenal seized on the space to make it 3-0 early in the second half with a fine finish from young Mexican forward Carlos Vela.
Portsmouth had started the brighter with Nadir Belhadj's fine run carving Arsenal in two but unfortunately for the hosts the Algerian's finish did not match his impressive build-up.
Arsene Wenger had made nine changes from the team that lost 1-0 against Manchester United in the Champions League semi-final first leg but the youngsters were quick to find their feet.
Vela stumbled under a challenge from Sol Campbell which looked like a penalty but referee Lee Mason awarded a corner.
Moments later Arsenal had an opener when Andrey Arshavin was allowed to have two attempts to cross the ball and he found Bendtner whose header squirmed past a red-faced James.
Portsmouth created another opportunity when Peter Crouch and Belhadj played a neat one-two for the England striker to fire over but soon Arsenal had a second.
They should have been awarded a penalty when Arshavin was clipped by Sylvain Distin but they were once again denied by Mason only for the referee to point to the spot five minutes later after the Russian was challenged fairly by Sean Davis.
Bendtner struck his penalty into the bottom left-hand corner and Portsmouth manager Paul Hart was hurried into making some rapid half-time adjustments.
Nigerian's Kanu and John Utaka were introduced and both had chances to find a way back into the game for their side.
Kanu placed his shot too close to Lukas Fabianski but Utaka's was even worse as he rounded the Polish goalkeeper but could not find his feet to tap into an unguarded net.
With Portsmouth wasteful, Arsenal killed the game off with a rapid switch from defence to attack culminating in Vela's fine finish across James.
The final 30 minutes were played at a pedestrian pace but still Arsenal had further chances through Bendtner and Vela before Noe Pamarot was dismissed 12 minutes from time for bringing Arshavin down when the Russian was clean through on goal.