Jake Virtanen scored the eventual winner for the Hitmen (12-6-4) in the second period and assisted on Kenton Helgesen's goal in the first. Pavel Padakin scored the other goal for Calgary.
Sam Fioretti and Tanner Eberle scored for the Warriors (7-16-4), who are winless in five games, and Miles Warkentine assisted on both.
Moose Jaw's Justin Paulic turned away 28-of-31 shots in a losing cause.
Calgary trailed 2-1 in the second before Padakin and Virtanen scored 54 seconds apart.
The Hitmen went 1 for 6 on the power play while the Warriors failed to score on five chances with the man advantage.