Nadget Fedoul saved the last penalty from Fereshteh Al Karimi to seal the win for the UAE.
The match had ended in a 2-2 draw after 90 minutes.
The UAE had tied the game in the 85th minute with a penalty by Dalila Zerrouki, who was awarded the spot kick after Iran's Vahideh Esari handled the ball in the box and was red-carded.
Iran striker Maryam Rahimi, the leading scorer in the tournament, had given the visitors a 2-1 lead through a penalty of their own, in the 54th minute. Rahimi earned the penalty when she was felled by the UAE goalkeeper Fedoul.
The UAE had first levelled the match in the 47th minute when Oumayma Maaouia, set up by Imen Trodi, unleashed a powerful shot from 25 yards.
Iran scored the opener in the 39th minute. Niloosar Ardallani, who was on the left side of the penalty area, sent a pass to Al Karami, who scored with a looping shot, beating the UAE's Fedoul.
Bahrain defeated Jordan 4-3 in a shootout in the third-place game after the match ended in a 0-0 deadlock.