Bendtner helped Arsenal extend their unbeaten league run to 21 matches
Arsenal booked their place in next season's Champions League with a win that means Portsmouth are still yet to secure their Premier League status.
Pompey goalkeeper David James gifted Arsenal the opener when he fumbled Nicklas Bendtner's header into his net.
The Dane then grabbed a second from the penalty spot after Sean Davis was ruled to have fouled captain Andrey Arshavin.
Carlos Vela lashed home a third before Noe Pamarot was sent off for bringing Arshavin down when through on goal.
Arsenal's victory moves them 13 points clear of fifth-place Aston Villa, who play on Monday, and they are now mathematically guaranteed to finish at least fourth.
They are unbeaten in 21 league matches and have scored at least three goals in each of their last five away league games, equalling a club record set in 1932.
Wenger praises Arshavin 'honesty'
Portsmouth are seven points clear of the relegation zone but need another six from the remaining nine available to make absolutely sure of their survival.
Their run without a victory over one of the 'big four' extends to 17 games but they will be confident of avoiding the drop, with Blackburn, Sunderland and Wigan their final three opponents.
Gunners boss Arsene Wenger clearly had an eye on his side's Champions League semi-final second leg against Manchester United on Tuesday, and made eight changes to the XI that started the first leg at Old Trafford in midweek.
But the visitors immediately settled into their usual rhythm early on and posed countless problems to a Portsmouth defence which struggled to cope with their attacking threat all afternoon.
Vela had a penalty appeal rejected when he was hauled over by Sylvain Distin - referee Lee Mason awarded a corner despite Distin appearing to make no contact with the ball - but Arsenal's pressure would soon tell.
Portsmouth could only clear the resultant set-piece straight back to Arshavin and his cross was met by Bendtner, whose header squirmed embarrassingly through James's hands and into the net.
But Portsmouth were not without chances of their own.
Inside the first 10 minutes, Nadir Belhadj broke clear of a brittle-looking Arsenal back four but sliced his shot horribly wide and Peter Crouch poked inches wide after fine build-up play.
Yet as the half wore on Arsenal assumed complete control and their advantage was doubled when Bendtner slotted into James' left-hand corner following Davis' challenge on Arshavin.
Replays suggested the midfielder might have got a toe to the ball as he slid in on Arsenal's stand-in captain and Portsmouth were furious with referee Lee Mason.
Missed chances 'hard to swallow' for Hart
Pompey caretaker manager Paul Hart introduced former Gunner Kanu and John Utaka at the break, and the hosts began the second half in determined fashion.
Utaka screwed wide from a glorious position before Crouch and Kanu went close with driven efforts and Utaka failed to get a shot away having rounded Lucasz Fabianski.
The home crowd were in full voice but they would soon be deflated as Arsenal broke away and Arshavin laid the ball back for Vela to lash into the bottom left-hand corner of James' net from the edge of the area.
Portsmouth continued to probe for a route back into proceedings and Fabianski was forced to tip a dipping Crouch effort over the bar before repelling a Distin volley from point-blank range.
But their day went from bad to worse when Pamarot was shown a straight red card for dragging Arshavin to the ground as he raced on to Aaron Ramsey's searching pass.
Portsmouth manager Paul Hart: "The boys are adamant that it was not a penalty for their second goal and I agree with them. There was no physical contact.
"I am not here to vilify referees. We have had a few decisions go against us recently but it is a tough life for referees and it is for us.
"Everyone around us in the table has lost today, so there is no change. We just have to look after ourselves."
Arsenal manager Arsene Wenger: "I wanted to give a breather to some of the players
"I have no doubts about the younger players because I see them every day and what we work on, you could see that on the pitch today.
"We were sharp, composed and mobile with a great attitude."
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