Brady Ramsay had a goal and an assist for the Hurricanes (8-7-1) while Jamal Watson chipped in with two assists.
Graham Hood added a single goal to round out Lethbridge's offence.
Adam Lowry scored the lone goal for the Broncos (6-7-4).
Ty Rimmer made 22 saves for the win as Eetu Laurikainen stopped 33-of-37 shots through 40 minutes of play to pick up the loss.
Landon Bow came in to play the third period and stopped all 13 shots he faced in relief.
Lethbridge went 1-for-7 on the power play while Swift Current failed to score on four chances with the man advantage.