Cody Sylvester and Peter Kosterman also scored for the Hitmen (14-5-3), who had five days off between games since losing 4-0 at home to the Kootenay Ice last Monday.
Graham Black scored both goals for the Broncos (9-11-5), who have lost two straight games and four of their past six.
Chris Driedger stopped 21-of-23 shots he faced in the Calgary net to improve his record to 11-3-2, while Swift Current goaltender Eetu Laurikainen made 28 saves in a losing cause.
The Broncos went 1-for-3 with the man advantage, while the Hitmen failed to score on two power-play chances.
Sylvester scored the lone goal of the first period when he took a pass from Greg Chase and made a slick backhand-to-forehand move to deke out Swift Current forward Tanner LeSann before depositing the puck past Laurikainen.
After a scoreless second period, Padakin put the Hitmen up 2-0 at 4:51 of the third period with a shorthanded goal.
Just 39 seconds later, Grant scored a power-play goal for the Broncos. Grant then scored an unassisted goal to tie up the game at 10:43.
Exactly two minutes later, Kosterman scored his second goal of the season when he slapped a shot to the top corner past Laurikainen.
Padakin then rounded out the scoring with an empty-net goal.