The 19-year-old forward put the home side in front on 18 minutes, but Wolves came back and were level on the stroke of half-time thanks to Benny Ashley-Seal’s penalty.
Liverpool replied immediately, Herbie Kane’s strike a minute later giving them a half-time lead.
Brewster’s second strike and an own goal from Dion Sanderson put Liverpool in command, but they had a nervous ending as Ashley-Seal and Boubacar Hanne scored late on for Wolves.
A first win in four lifts Liverpool to seventh on nine points, two places and one point above Wolves.
See: Liverpool report
Liverpool: 26 Oct v Blackburn (H)
Wolves: 26 Oct v Spurs (H)