Tambellini scored his first goal 6:20 into the game and added his second 5:17 into the second period. He also tacked on two assists for a four-point night as the Hitmen took a 2-1 lead in the best-of-seven, second-round series.
Travis Sanheim scored on the power play and set up two more for Calgary, Connor Rankin and Kenton Helgesen each had a power-play goal and an assist apiece, and Mack Shields stopped 29 shots.
Chad Labelle scored twice for Medicine Hat, which found the back of the net twice in the third period to pull to within one goal. Dryden Hunt and Steven Owre also scored and Marek Langhamer made 26 saves.
The Tigers host Game 4 on Wednesday.