Trevor Cox had a goal and two assists for the Tigers (16-19-2) while Dylan Bredo, Miles Koules and Boston Leier each scored once.
Coda Gordon scored the lone goal for the Broncos (17-18-5), who lost for the first time in four outings.
Landon Bow took the loss after allowing three goals on 13 shots through 34 minutes of action. Steven Myland stopped all 13 shots he faced in 25 minutes of relief.
Medicine Hat went 1 for 5 on the power play while Swift Current failed to score on three chances with the man advantage.