Marek Langhamer kicked out 39-of-41 shots for the Tigers — including all 13 his way in the extra period — as Medicine Hat evened the series at a game apiece.
Dryden Hunt and Steven Owre found the back of the net for the Tigers in regulation.
Travis Sanheim scored for the Hitmen and picked up an assist on Jordy Stallard's goal that tied the game 2-2.
Calgary's Mack Shields made 47 saves in defeat.
Medicine Hat went 1 for 2 on the power play while the Hitmen failed to score on four chances with the man advantage.
Game 3 goes Monday in Calgary.