A first-half double from Sergio Gomez put Spain in charge in Kolkata, but Liverpool striker Brewster's expertly-taken header shortly before the interval halved the Young Lions' deficit.
Morgan Gibbs-White then struck a 58th-minute equaliser and Phil Foden put England in front 11 minutes later.
Steve Cooper's side were not finished, though, as late goals from Marc Guehi and Foden put the gloss on an incredible turnaround and confirmed their status as world champions.
Brewster finished the tournament as top scorer, with seven of his eight goals coming in the quarter-finals, semi-finals and final.