The 19-year-old forward now has 13 goals in 41 games and four of them have been game winners, which is the third most of any WHL player.
Pavlo Padakin, Zane Jones and Greg Chase also scored for the Hitmen (27-10-4), who have won three games in a row, while Spencer Humphries, Alex Roach and Chase Clayton each had two assists.
Brett Kulak led the Giants (11-30-0) offensively with a goal and two assists and Cain Franson, Riley Kieser and Jackson Houck had a goal apiece.
Mack Shields made 22 saves for the win as Payton Lee turned aside 29 shots in defeat.
Calgary went 2 for 3 on the power play while Vancouver scored twice on seven chances with the man advantage.
Kieser and Franson counted first-period goals for the Giants as Vancouver built up a 2-1 lead.
Padakin and Chase then scored goals in the second period for Calgary before Brassart put the Hitmen up 4-2 early in the third.
Kulak then assisted on a power-play goal by Houck before wiring a long-range shot of his own past Shields to tie up the game at 4-4.
Brassart swatted a rebound past Payton at 10:39 of the final period with the Hitmen on the power play to put his club ahead for good.