American Walker Zimmerman blocked England forward Harry Kane's shot in the six-yard box in the 10th minute at Al Bayt Stadium.
US midfielder Weston McKennie missed a chance to score despite shooting from close range at the opposition's goal in the 25th minute.
Chelsea's US-based winger Christian Pulisic's left-footed long shot hit England's crossbar in the 32nd minute.
Pulisic wasted another chance with a misplaced header in the 42nd minute.
England's Bukayo Saka shot wide in the penalty area in the 44th minute.
US goalkeeper Matt Turner tipped the accurate shot of Mason Mount to the corner in the 46th minute and the first half ended without a goal.
In the second half, Marcus Rashford's long-range shot was saved by Turner in the 86th minute.
Kane wasted another chance to score for England with an inaccurate header in the 93rd minute.
England leads Group B with 4 points. Iran is second with 3. The US is behind in third with 2 and Wales bottoms out the group with one point.
