Pulisic was back on his feet after receiving treatment for a few minutes but did not look comfortable and he was replaced by Brenden Aaronson at the break after sustaining an abdominal injury, in a major blow for the Americans' knockout stage hopes.
U.S. coach Gregg Berhalter said the Chelsea forward was taken to hospital as a precaution. His team, who drew their first two games, will face three-times finalists Netherlands on Saturday for a place in the quarter-finals.
The Americans finished two points behind Group B winners England to reach the last 16 for the fifth time since 1994. Iran finished third with three points, with Wales bottom with one point.
"In the first half we showed what we can do, soccer wise. We had a really good first half. Second half we showed what we could do determination wise. The guys grinded, gave every single ounce and we are undefeated going into the next round," Berhalter said.
Berhalter's team, the second youngest at this year's finals, may lack experience on the big stage but they stepped up and delivered a commanding performance when their spot at the World Cup was on the line.
Knowing that only a win would keep them in the tournament, they pressed with high intensity from the first whistle - their full backs almost playing as wingers - and chances flowed thanks to their slick attacking style.
Tim Weah, who spurned two glorious opportunities before Pulisic put the Americans ahead, had the ball in the net late in the first half but his strike was ruled offside.
Iran only needed a point to advance but they were largely restricted to playing on the counter and unable to muster a credible attempt at scoring until the second half.
Substitute Saman Ghoddos, who replaced Sardar Azmoun at half time, almost pulled Iran level after meeting a superb cross from Ramin Rezaeian while Morteza Pouraliganji met a free-kick with a diving header that went just wide deep in stoppage time.
Mehdi Taremi appealed for a penalty in the closing stages as he went down with Cameron Carter-Vickers trying to stop him and his team mates surrounded the referee but their protests were waved away as Iran ultimately failed to register a shot on target.
Politically charged
The build-up to Tuesday's match was overshadowed by more than four decades of sour relations between the two countries and the civil unrest that has gripped Iran since the September death of 22-year-old Mahsa Amini in police custody.
Iran's players, pressured by protesters to side with them publicly and condemn a deadly state crackdown, declined to sing the national anthem in their opening match against England but sang before their victory over Wales and again on Tuesday, where they were loudly jeered by their supporters.
Relations between Washington and Tehran, who severed all formal diplomatic ties in 1980 after the Islamic Revolution, have worsened since 2018. The U.S. has imposed sanctions on Iranian officials over the crackdown on protesters.
On the eve of this eagerly awaited rematch, Berhalter had urged for focus to be redirected to soccer. His players did exactly that, and blocked out the stormy exchanges to secure the win they needed to stay alive in the tournament.