Luke Philp had a goal and an assist for the Ice (17-24-1), who extended their win streak to seven games, while Jaedon Descheneau added three assists.
Joey Leach, Levi Cable and Tanner Faith each chipped in with two assists for Kootenay.
Elgin Pierce had two goals and an assist for the Tigers (19-21-3) and Boston Leier scored once and set up two more.
Curtis Valk and Logan McVeigh added single goals to round out Medicine Hat's offence.
Mackenzie Skapski started in goal for the Ice but was pulled after allowing four goals on 12 shots through 24 minutes of action. Wyatt Hoflin stopped 26-of-27 shots in relief to earn the victory as Cam Lanigan made 32 saves in a losing cause.
Kooteny went 3 for 5 on the power play while Medicine Hat scored once on five chances with the man advantage.