Goals from Rouzbeh Cheshmi and Ramin Rezaeian left Wales fighting to save their World cup dream as Wayne Hennessey was sent off following a violent tackle on Taremi.
Iran showed they wanted the win much more than their European contingents as they hit the post twice in quick succession. Azmoun was the first and Gholizadeh the second.
Wales goalkeeper, Hennessey became the first player to be sent off in the Qatar tournament for clattering into Mehdi Taremi late in the game.
Iran, who would have been eliminated with a defeat, instead climbed to second in Group B behind England, against whom they had lost 6-2 in their opening game.
Wales tumbled to the bottom of the group and will have to defeat neighbours England in their final match next week to have any chance of reaching the knockout phase in their first World Cup since 1958.
The United States take on England later on Friday.
The Iran players opted to sing the national anthem in contrast to their stance before the game against England, when they remained silent in an apparent gesture of solidarity with anti-government protestors.
Some Iranian fans were in tears during the anthem.
– Wales start brightly –
Wales manager Rob Page elected to start striker Kieffer Moore after his impressive appearance as a substitute against the USA.
The Bournemouth man’s flick-on led to an early effort from Neco Williams that flew just over the crossbar.
The Welsh carved out the first clear chance in the 12th minute as Moore stretched to volley Connor Roberts’ cross, but goalkeeper Hossein Hosseini was able to parry his effort.
Iran thought they had taken the lead minutes later, although Ali Gholizadeh was clearly offside before he tapped in and the goal was ruled out by VAR.
A cagey game burst into life with a crazy 20-second spell shortly after half-time. Sardar Azmoun sped clear of the Welsh defence but saw his shot come back off the post.
The ball was recycled to Gholizadeh, who cut inside and curled an excellent strike from outside the box, which bounced away off the other upright, with Azmoun’s follow-up saved by a floored Hennessey.
Iran suddenly looked like scoring every time they went forward and Ethan Ampadu had to make an excellent block to deny Taremi the opening goal.
Wales had Hennessey to thank for staying on level terms with 17 minutes left, as he stretched to tip Saeid Ezatolahi’s low shot around the post.
The game opened up in the final minutes as both sides knew they likely needed more than a draw.
Iran were given a huge boost in their push for a winner when Hennessey recklessly charged out of his goal and crashed into Mehdi Taremi in the 86th minute.
Remarkably, Guatemalan referee Mario Escobar only initially booked the ‘keeper, but that was corrected after a VAR review and Hennessey was dismissed.
Leicester’s Danny Ward took his place and quickly saw Mehdi Torabi’s effort fly past his post.
But an emotional day for Iran and their fans were given its crowning moments right at the death when Cheshmi hammered home from the edge of the box and Rezaeian raced clear to clip over Ward.