The 17-year-old opened the scoring as early as the 11th minute, reacting quickly to turn the ball home after an attempt from Phil Foden had been palmed out.
Brewster then doubled his and his country's tally three minutes later, sprinting onto a through-ball from Morgan Gibbs-White and dinking a finish over the onrushing goalkeeper.
Steve Cooper's team were forced to wait until the second half for their next goal but, again, Liverpool's talented young striker had a hand in it.
He returned the favour for Gibbs-White's earlier assist following a quick break, firing in a low cross that his colleague finished with aplomb.
The USA pulled a goal back late on, Josh Sargent scoring from close range, but the Young Lions restored their advantage with the final kick of the game.
Having been upended in the box in injury time, Brewster brushed himself down and fired a confident penalty into the bottom corner to seal his hat-trick.