DPR Korea was reduced to 10-man in the 66th minute after its midfielder Kye Tam was shown his second yellow card.
Mohammad Mehdi Mohebi opened the scoring for Iran in the 73rd minute and Mehdi Taremi made it 2-0 four minutes later. Hosseinzadeh completed the scoring three minutes into injury time with a composed finish on the run.
Amir Ghalenoei’s Iran ended the qualification as the first team with 23 points, two points above Uzbekistan, who defeated Qatar 3-0 earlier in the day.
Iran had already confirmed its ticket to next year's FIFA World Cup to be hosted by Canada, Mexico and the United States.