Samir Nasri and Emmanuel Eboue were also on target as Arsenal completed a 6-2 aggregate victory to reach the last eight for the third consecutive season.
Bendtner was guilty of a series of bad misses in the Premier League win over Burnley at the weekend but he answered his critics in style with a commanding performance to crown a dazzling display by manager Arsene Wenger's side.
"It shows how quickly football can change," Wenger told Sky Sports. "I hope it won't give him too much confidence now.
"But it's good for him especially after Saturday. I hope it will give him the desire to work even harder."
NEWS: Wenger faith in Bendtner pays off
Porto had never won a European fixture in England before but Arsenal's poor record of overturning first-leg deficits, a feat they had not managed for more than 30 years, gave the Portuguese side hope of defending their 2-1 advantage.
CHILLY NIGHT
That hope did not last long on a chilly north London night as they were completely outclassed.
"They controlled the match," Porto coach Jesualdo Ferreira told reporters. "They played very well but I don't think we deserved to lose by five goals.
"Arsenal are very good at provoking the opportunities they need and they have the quality to seize those moments. This defeat hurts."
Injured Arsenal skipper Cesc Fabregas, whose midfield playmaking role was filled superbly by Nasri, said in his programme notes he hoped Bendtner had saved his goals for Porto after his blunders against Burnley.
After 10 minutes the Danish striker duly obliged when he slotted the ball into an empty net after keeper Helton had bravely denied Andrei Arshavin who had been released by Nasri.
Arshavin's pace and trickery teed up Bendtner for his second on 25 minutes as Arsenal moved ahead on aggregate.
Porto enjoyed a brief spell of pressure early in the second half but after Falcao failed to convert their best chance of the night after being set up by Hulk, normal service was resumed.
Two goals in four minutes just past the hour killed off the visitors. After 63 minutes Nasri ran at pace into the Porto area and dribbled past three mesmerised defenders before steadying himself and planting a shot inside the far post.
Then Arshavin carved Porto open and his reverse pass allowed Eboue to skip around the despairing Helton and roll the ball into an unguarded net.
Bendtner completed his first Arsenal hat-trick with virtually the last kick of the game, firing a low penalty into the corner after Eboue was brought down.
Porto may have had Hulk in their ranks but for one night at least, the much maligned Dane was Arsenal's super-hero.
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