The Chelsea striker grabbed the only goal of the game in the 38th minute when he bravely stole in to convert a headed cross by Sergino Dest from point-blank range.
Iran summoned little in search of the equaliser that would have sent them through to a second-round clash with the Netherlands, with only a late diving header from Morteza Pouraliganji and a last-gasp VAR check causing American hearts to flutter.
The US dominated the opening period to such an extent that the only fear was whether they would live to regret a catalogue of missed chances as they once again lacked cutting edge in the final third.
Yunus Musah drove an early shot over the bar and a good Pulisic header was saved by Iranian keeper Alireza Beiranvand, who also scrambled clear from a Dest cross.
Exploiting plenty of space on the flanks, Dest was proving the major threat for the US whilst the Iranians, looking to make it through the group stage for the first time at the sixth attempt, offered little.
American woes in front of goal continued when Timothy Weah snatched at a header when unmarked on the edge of the six-yard box, before the same player drilled another good opportunity over the bar.
Weston McKennie sparked the breakthrough the US deserved shortly before the break with a brilliant cross-field pass to find Dest, who deftly flicked the ball into the path of Pulisic.
Weah found the net but was judged marginally offside in the process, while the withdrawal of Pulisic, who had been injured in the process of scoring, suggested a long second half in store for Gregg Berhalter's men.
Iran certainly carried more threat in the form of Brentford striker Saman Ghoddos, on for the ineffective Sardar Azmoun, and he had Iran's best chance in the 52nd minute when he met Ramin Razaeian's excellent right-wing cross with a header that flashed just wide of target.
After Pouraliganji's header, which went the wrong side of Matt Turner's right-hand post in the third of nine added minutes, the US also had to survive a late VAR check when Mehdi Taremi crumbled under the challenge of Cameron Carter-Vickers in the box.