Iran, who have never reached the World Cup knockout stage in their previous five attempts, needed at least a draw to secure four points for their progress. Pressed by the U.S. initially, Iran created few chances but maintained a solid formation.
The opener came in the 38th minute when Chelsea winger Pulisic bundled the ball home in very close range thanks to Sergino Dest's cross from the right side.
Timothy Weah almost enlarged the advantage for the U.S. when he scored late in the first half before being denied by VAR because of an offside.
Iran strengthened their attack as Saman Ghoddos nodded a deflected right-wing cross at the back post but could not steer it on target in the 52nd minute.
In the final minutes, the U.S. dropped deeper and deeper to defend the opponents' attacks better. A one-goal victory could assure them a slot in the last 16 while Iran once again failed to qualify.
As Group B runners-up, the U.S. will play against Group A winners the Netherlands in the round of 16 at Khalifa International Stadium on Saturday.