Alex Roach also scored for the Hitmen, and Cody Sylvester helped out with three assists.
Turner Elson and Dominik Volek scored for the Rebels, who will attempt to even things up when Calgary hosts host Game 2 of the series on Friday.
Chris Driedger made 28 saves for the Hitmen, while Patrik Bartosak stopped 29 shots for the Rebels.
Calgary went 2-for-5 on the power play, while Red Deer failed to score on three chances with the man advantage.
Brassart scored the only goal of the first period before Roach notched a power-play goal at 1:21 of the second to put the Hitmen up 2-0. Just 36 seconds later, Volek responded for Red Deer before Brassart scored back-to-back goals to put the Hitmen up 4-1 through two periods.
Elson scored at 7:02 of the third to pull Red Deer within two, but that was as close as the Rebels would get.