In the match, held at the Jassim Bin Hamad Stadium in Doha, Qatar, Riad Benayad found the back of the net with a right-footed shot from the center of the box in the 43rd minute.
Iran captain Alireza Jahanbakhsh leveled the score after receiving a ball from Omid Noorafkan into the six yards in the 64th minute.
With seven minutes remaining, Mohamed Amoura scored the winner after Noorafkan failed to clear the ball outside the box.
Team Melli played Algeria as part of preparation for the 2022 FIFA World Cup.
Iran has been drawn in Group B along with England, the US and Wales.