Jurgen Klinsmann's side were forced to work hard in Utah to claim their fourth straight victory and it was not until the 73rd minute that Altidore scored a left-footed strike at the far post courtesy of Fabian Johnson's assist.
It was Altidore's fourth goal in the six-team final round, and it put America on 13 points, two clear of Costa Rica, who beat Panama 2-0.
Panama midfielder Armando Cooper hit the bar with a long-distance effort two minutes before the break.
But the Ticos took the lead quickly in the second period, as Bryan Ruiz netted a free-kick in the 49th minute, before Celso Borges widened the gap from outside the box two minutes later.
Costa Rica sit three points clear of Mexico, who occupy the third and final qualification spot and are themselves one ahead of Honduras, after six games.