Sardar Azmoon took a brilliant pass from Ashkan Dejagah with his back to goal, spun Qatari defender with a sharp turn and finish in the 52nd minute to ensure Carlos Queiroz's side will progress from Group C with the UAE.
But, Iranian starlet was sent off 10 minutes later because of serious injury, it seems he will miss the remainder of the Asian Cup.
Iranian footballers missed several chances for netting the ball, but Rubin Kazan striker's goal was enough for Carlos Queiroz's men to secure a spot in the next round of the the tournament.
Before Iran's victory, the UAE, who routed Qatar 4-1 in their opening fixture, defeated Bahrain 2-1 at Canberra Stadium.
At the end of the second matches, the UAE stood atop Pool C with 6 points followed by Iran (6 points), Bahrain (0) and Qatar (0).
Iran and Qatar have played each other 20 times, with Iran winning 12 matches, Qatar taking 3 victories and 5 others ending in a draw.
Iran had defeated Bahrain in their first match of Group C of the 2015 AFC Asian Cup in Australia on Sunday. The three-time champions were impressive against Bahrain with leopards providing a fine combination of power and skill, while Queiroz's men also looked solid in defence. They missed several chances for netting the ball, and the goals from Hajsafi and Shojae sealed a victory for Iranian side.
Iran has been drawn in Group C along with Bahrain, the UAE and Qatar. Persian Leopards will play with the UAE in their next match on Monday, while Qatar are due to stand against Bahrain.
Asia's highest-ranked side had played just twice since bowing out in the group stages of the 2014 World Cup in Brazil, beating South Korea 1-0 last November before edging out Iraq by the same scoreline in January.
Iran's preparations took a hit last week when Hashem Beikzadeh broke his hand in training, compounded by the fact fellow defender Pejman Montazeri is out of the tournament due to a calf injury. Beikzadah also had missed the 2014 World Cup with a muscle complaint.
This is Iran’s 13th AFC Asian Cup finals appearance. Iranians have won the AFC Asian Cup title in 1968, 1972 and 1976, and scored 112 goals in the AFC Asian Cup. Team Melli has not progressed past the Asian Cup quarterfinals since 1996, falling well short of its most successful era, when it won three successive tournaments from 1968 to 1976.
The Islamic Republic of Iran climbed five positions in the new edition of the FIFA rankings to land in the 51th spot in the world, and stood at the first spot among Asian teams.
Iran is followed by Japan (54th), Korea Republic (69th) and Uzbekistan (74th) as the second, third and fourth teams of Asia.
