It was after 38 minutes that Sergino Dest headed the ball down to Christian Pulisic, 24, who shot in the lead goal and at the same time crashed into goalkeeper Alireza Beiranvand.
Pulisic was clearly hurt, but initially continued to play.
At half-time, however, he had to be replaced in favor of Leeds player Brendan Aaronson.
At the end of the first half, Timothy Weah also had the ball in the goal, but it was disallowed for offside.
Iran were more lively in the second half and pushed for an equaliser, but it never came.
At the very end, Iran wanted a penalty, but the referee acquitted.
- Iran came out as a new team after halftime and have dominated, said SVT Sports expert Markus Johannesson.
Thus, the country can continue to hope for a first advancement from a WC group stage.
The USA will face the Netherlands in the round of 16.