Brewster scored in the 11th, 14th and 90+6th minutes from a penalty while Morgan Gibbs White scored in 64th minute to hand England the convincing win.
A wasting a handful of chances, USA managed to score a consolation goal in the 72nd minute through Joshua Sargent.
England will face the winner of tomorrow's another quarterfinal duel between Brazil and Germany in the last-four round in Guwahati on October 25.
USA had the first shot at the goal in the second minute when Andrew Carleton's right footer from outside the box just missed the right corner of the England goal.
More From This Section
Timothy Weah's right-footer then missed the target by a whisker as USA continued to flounder chances.
England took the lead in the 11th minute through Rhian Brewster whose right-footed shot from the centre of the box slammed on to the top right corner of the American goal.
Three minutes later Brewster scored his second goal of the day with a brilliant scoop from the right side past an onrushing American goalkeeper to make the scoreline 2-0 in favour of England.
Down by two goals, the Americans went on the offensive and had a few clear chances but Andrew Carleton, Timothy Weah and Taylor Booth missed the targets.
It was an end-to-end battle between the two teams but both the sides were guilty of missing great chances.
USA's Joshua Sargent then hit the bar with a right footed shot in the 23rd minute.
Two minutes later, USA's Ayo Akinola was denied by cross bar.
The match continued to be an attacking display of football as both England and USA created numerous scoring chances.
The American goalkeeper Garces made a handful of saves to keep his side in the hunt in the second half.
An attacking England took the game away from USA in the 64th minute when Morgan Gibbs-White scored with a right-footer to the bottom right corner of the American goal after being assisted by Brewster.
Sargent reduced the margin for the Americans in the 72nd minute with a right-footed shot from close range to the bottom left corner of the English goal.
But Brewster added salt to USA's wound when he converted from a spot kick in the additional time to register his hat- trick and a convincing victory for his side.