Atlanta United defender Miles Robinson headed in after 118 minutes in Las Vegas, his third international goal.
The US win is their first in the tournament for North American, central American and Caribbean countries since 2017.
“I don’t know really what happened – some crazy emotions but I’m happy we got the W,” said Robinson.
“We were focusing a lot on set pieces. I knew if I could get open, I could finish one and Kellyn [Acosta] put a perfect ball in so I had to finish it.”
Mexico – the only nation to have won the tournament more often than the US – had the better of the first half and had a promising chance saved when a Rogelio Funes Mori header was turned round the post by US keeper Matt Turner.
Paul Arriola was in on the Mexico goal for the US shortly afterwards but hit the outside of the post, although the miss did not ultimately prove costly as his side went on to win.