The Philadelphia Union teenager produced a stunning lob in the 62nd minute to surpass Mathis Albert's record, which had stood for only five days.
Albert had become the youngest scorer in United States men's national team history at 17 years and 131 days when he scored against Chile on Wednesday.
Sullivan needed only one appearance to take the record for himself, intercepting a pass from Mexico goalkeeper Raúl Rangel before lifting the ball over him from distance.
“I just remember chipping the ball, hoping it didn't hit the crossbar or go over,” Sullivan said.
“I was getting nervous when it was in the air and then everything was a blur.”
The goal doubled the USA's advantage after Julian Hall had opened the scoring in the 28th minute. The 18-year-old forward continued his impressive start to international football, while Malik Tillman completed the victory in the closing stages.
US Soccer confirmed that the result was the Americans' third straight victory of the international window, with the 3-0 win coming in the 80th meeting between the two countries.
Sullivan is already one of the most closely watched young players in the United States. The midfielder currently plays for Philadelphia Union but is due to join Manchester City next season after the English club secured his signature as a 14-year-old in 2024.
His future in Manchester has nevertheless become less certain after City were found guilty of breaching the majority of the 115 financial rules they had been accused of breaking. The club are expected to appeal the findings.
For now, Sullivan's focus is on making the most of his rapid rise with the United States.
“These are the moments you dream of when you're a three, four, five or six-year-old,” he said.
“I manifested this moment, not just these past couple of hours when I found out I was starting, but my whole life.”
Mexico's night became even more difficult when substitute Luis Chávez was sent off in the 68th minute for putting his hand into Sebastian Berhalter's face.
The USA were already in control by then, but Sullivan's landmark goal had provided the defining moment of the evening.
At just 17, he now has a piece of US football history and another significant milestone on the road to his expected move to Manchester City.