Roach fired a slap shot past Swift Current goalie Eetu Laurikainen to give the Hitmen a 1-0 lead in their opening round best-of-seven series against the Broncos.
Brady Brassart had a hat trick for the Hitmen, while Brooks Macek and Colten Mayor also scored. Greg Chase had two assists.
Ryon Moser, Graham Black and Coda Gordon each had a goal and an assist for the Broncos, who will attempt to even things up when the Hitmen host Game 2 of the series on Friday night at the Scotiabank Saddledome.
Adam Lowry and Levi Bews also scored for Swift Current, while Colby Cave and Dillon Heatherington had two assists each.
Chris Driedger made 23 saves in the Hitmen net to record the win, while Laurikainen stopped 32-of-38 shots he faced at the other end of the ice.
The Hitmen went 1 for 2 on the power play, while the Broncos scored twice on five chances with the man advantage.
Macek scored a power-play goal for Calgary just 34 seconds into the game before Brassart put the Hitmen up 2-0 with 54.7 seconds left in the first period.
Mayor and Brassart then scored goals 16 seconds apart early in the second period before the Broncos reeled off three straight goals by Lowry, Moser and Bews to pull within a goal.
Brassart scored his hat-trick goal at 3:47 of the third period before Gordon responded for Swift Current 33 seconds later.
Black then notched a power-play goal for the Broncos at 13:53 of the third to force overtime.