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."
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.
"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."
Arshavin's pace and trickery teed up Bendtner for his second on 25 minutes as Arsenal moved ahead on aggregate.
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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