Brock Montgomery scored twice for Kootenay (22-25-1) in the second period to tie the game before Philp scored the winner at 13:52 in the third.
A power-play goal from Hunter Shinkaruk in the first period gave Medicine Hat (23-23-3) the lead, and Dylan Bredo added another in the second.
Mackenzie Skapski made 21 saves in net for the Ice, while Cam Lanigan stopped 20 shots.
Kootenay has won 12 of its last 13 games and seven straight at home. The Tigers meanwhile had their winning streak stopped at three games.