Sullivan, who is poised to join English Premier League side Manchester City next year, doubled the US lead with a long-range chip after Mexico goalkeeper Raul Rangel mishit a pass to the American outside his area.
"These are the moments you dream of when you're three, four, five or six-years-old," Sullivan said. "I manifested this moment, not just these past couple of hours when I found out I was starting, but my whole life."
Of the goal itself, he said: "I just remember chipping the ball, hoping it didn't hit the crossbar or go over. I was getting nervous when it was in the air and then everything was a blur."
Sullivan's strike came after 18-year-old Julian Hall had given Mauricio Pochettino's side the lead in the 28th minute. Hall's goal was his third in as many games since being handed his international debut in last week's defeat of Peru, and he also scored in Tuesday's 4-2 victory over Chile.
The record Sullivan broke belonged to Albert, aged 17 and 31 days, who scored in that Chile match.
Mexico dominated possession and territory early but could not find a way through a well-organised US defence. Gio Reyna set up the opening goal, surging into the penalty area and crossing low; Rangel parried the ball but only as far as Hall, who lashed in from close range.
Mexico's best chance came early in the second half when Roberto Alvarado's shot from the edge of the area was tipped over the bar by US goalkeeper Diego Kochen. The visitors' night worsened when substitute Luis Chavez was shown a red card late on.
The loss piles more pressure on Mexico coach Rafael Marquez, who is still seeking his first win since taking over following the World Cup.