Midfielder Christian Pulisic, long dubbed as the face and future of American soccer, scored the match's only goal in the 38th minute of play.
Pulisic collided with Iranian goalkeeper Alireza Beiranvand on the goal and was helped off the field by USMNT trainers before returning to the match several minutes later.
The Americans held a 51% possession advantage, as well as an 12 to 3 advantage in shots and 5 to 0 edge in shots on goal.
The USMNT faced a must-win scenario trailing Iran by one point ahead of its final match of Group B play.
The Americans finished Group B play with five points, while Iran finished with three points, following Monday's match.
England secured the top Group B seed with seven total points.
The USMNT tied both Wales and England in their first two matches of Group B play to earn three points prior to Monday's win.
Tim Weah scored the American's first and only goal prior to Monday's match on a throughball assist by Pulisic in the 35th minute of play in the 1-1 tie against Wales last Monday (November 21).
Weah, 22, became the first American player born in the 2000s to score a goal during World Cup play.
The Americans held England scoreless in their second match of Group B play last Friday (November 25).