Benji Kimpioka had given the hosts a second-half lead but Brewster forced an own goal from Michael Collins before the 19-year-old won and converted a late penalty.
Fulham went ahead at Motspur Park through Fabio Carvalho, Jayden Harris and Tayo Edun.
But Joseph Hungbo, Kaylen Hinds and Sonny Blu Lo-Everton pegged them back before Hungbo scored a second with 18 minutes remaining.
In the other match in the group, Everton were denied a first win of their PL Cup defence by Plymouth Argyle goalkeeper Mike Cooper in a 1-1 draw.
Cooper was beaten by Harry Charsley but, after Billy Clarke equalised, he starred with saves from Oumar Niasse, Kyle John, Ellis Simms and Ryan Astley.
Watford top the group on four points, followed by Fulham, Plymouth and Everton.
It was 1-1 at the break after goals from Southampton's Kornelius Hansen and Forest's Alex Mighten.
Saints moved to four points from two matches thanks to second-half strikes from Jake Vokins and Christoph Klarer.
Forest are bottom, two points behind Stoke City.