The Young Lions went behind eight minutes in when Chelsea prospect Marc Guehi inadvertently turned a wicked corner delivery into his own net.
But just two further minutes had elapsed by the time Brewster found space in the Norwegian box to sidefoot Jadon Sancho's unselfish pull-back home and level the scores up.
The 17-year-old then doubled his and his country's tally just past the half-hour mark, firing in an emphatic left-footed finish from another Sancho pass.
Phil Foden made the game safe late in the second half as Steve Cooper's side kicked off their bid for glory in Croatia with a 3-1 victory.