Tim McGauley had the other goal for Brandon (7-5-2), which got 27 saves from Corbin Boes.
Jackson Houck had a goal and an assist for Vancouver (2-9-0), which owns the WHL's worst record.
Brett Kulak also scored for the Giants, while Payton Lee made 25 saves in defeat.
Buonassisi tied the game in the second period and scored a go-ahead goal on a power play early in the third.
McGauley scored the eventual winner at the five-minute mark of the final period for the Wheat Kings, who moved into second place in the East Division.
The Giants opened the scoring early in the first when Houck hopped on a loose puck and beat Boes for his third of the season at 2:03.
The Wheat Kings got the equalizer midway through the second period when Buonassisi elected to shoot 2-on-1, snapping a shot past Lee.
Two power-play goals in 78 seconds decided the game early in the third.
With David Musil off for high sticking, the Wheat Kings took their first lead of the game at 3:42. Ryan Pulock put the puck towards the goal and it found its way to Buonassisi, who buried his second of the night and sixth of the season.
The Wheat Kings then made it 3-1 when Rene Hunter's shot was stopped but the rebound bounced right to McGauley at the side of the goal.
The Giants made a game of it at 15:28 when Houck skated hard to the net before dishing to Kulak.
Vancouver got a late power play but could do nothing with it as Brandon held on.
The Wheat Kings finished 2-for-4 with the man advantage, while Vancouver was 1-for-4.