England will meet either Spain or Mali in the final on Saturday.
Barcelona's Abel Ruiz put his side ahead from the penalty spot after 19 minutes and the captain doubled Spain's lead in style before the break, latching onto Cesar Gelabert's fine throughball before rounding the goalkeeper and finishing.
African champions' Mali's lone goal came through Lassana N'Diaye in the 74th minute.
However, that was too little too late and Spain cruised into the final.
In striking his second treble in succession, he became the first player to score consecutive hat-tricks in the quarter-finals and semi-finals of the competition since Marcel Witeczek in 1985.
Mali will now face Brazil for the third-place play-off before the final at Kolkata's Salt Lake Stadium.
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"It was a great team performance".
The constant attacks and counter-attacks saw the ball travelling fast at both ends, with the bulk of the spectators rooting for Brazil.
England U17 take on Brazil on Wednesday, October 25. "And obviously they are going to go and play the ultimate game - the final". Morgan Gibbs White won the ball from Brazilian right-back Wesley and fed Callum Hudson-Odoi, who in turn set up Brewster. Gabriel Brazao produced a fine reaction save, but the Liverpool teenager was first to the rebound.
Notably, all three of his goals were converted from inside the six-yard-box and Brazil were powerless to prevent Brewster's predatory instincts in front of goal. Receiving a cross, Wesley struck up a fine combination with Paulinho, and then let loose a right footer which was only partially saved by Anderson.
However, the relief in the Brazil benches lasted only 18 minutes.
Arsene Wenger will find it tough to keep Nketiah on the sidelines for much longer, and Jurgen Klopp should start considering giving Brewster opportunities too when he is back available.
As the English defence soldiered on, Brewster was on target to give a further cushion to his team.