It was Vasilevskiy's second shutout of the season and his 42nd in the NHL.
Darren Raddysh and Anthony Cirelli scored for the Lightning (33-14-4), who are 15-1-1 in their past 17 games, and have won six straight at home. Nikita Kucherov had two assists to extend his point streak to six games (three goals, 10 assists).
Karel Vejmelka made 26 saves for the Mammoth (27-21-4), who had won five straight and ended a nine-game point streak (8-0-1). They play the second of a back-to-back set at the Florida Panthers on Tuesday.
Raddysh gave the Lightning a 1-0 lead on the power play at 17:38 of the second period. He finished a cross-ice pass from Kucherov with a one-timer from the top of the left face-off circle over Vejmelka's glove. It was his eighth power-play goal, which leads all defensemen.
Vasilevskiy, who has won 12 of his past 13 starts (12-0-1), stopped Clayton Keller on a breakaway at 10:15 of the third period to preserve the lead. Keller collected the puck in transition, broke in alone and tried to slide a backhander five-hole.
Utah did not score after going on a power play at 13:16 and went 0-for-3 with the man-advantage.
Cirelli pushed the lead to 2-0 with a power-play goal at 19:14 with a wrist shot from the slot that squeaked through Vejmelka and fluttered into the net.
