Dylen McKinlay and Colton Sissons also scored for the Rockets (8-6-2), who wrapped up their four-game road trip though Alberta with a 2-1-1 record.
Brendan Hurley scored the lone goal for the Hitmen (8-4-3), who have lost three straight games and four of their past five.
Kelowna goaltender Jordon Cooke made 21 saves to record the win, while Calgary's Mack Shields stopped 25 shots in a losing cause.
Neither team recorded a power-play goal as the Rockets went 0-for-3 and the Hitmen went 0-for-6.
Although they were outshot 8-3 in the opening period, the Hitmen led 1-0 on Hurley’s first goal of the season.
Franko and McKinlay then scored goals 62 seconds apart in the second period to give the Rockets a 2-1 lead after 40 minutes of play.
Franko added an insurance goal in the third period and Sissons rounded out the scoring with an empty-net goal.