Dylan Guenther gave Utah a 1-0 lead at 7:27 of the first period. Cooley skated down the left wing and passed back up to Guenther, who scored blocker side with a wrist shot from the high slot.
Alexander Wennberg tied the game 1-1 at 14:58, taking a pass from Barclay Goodrow just inside the blue line before beating Vejmelka over his glove with a wrist shot from the left circle.
Mikael Granlund gave the Sharks a 2-1 lead at 14:11 of the second period. Zetterlund's shot from the slot hit off the leg of Sergachev and deflected to Granlund, who scored off the outstretched glove of Vejmelka from the bottom of the left circle.
Schmaltz tied the game 2-2 at 18:52 with a power-play goal, one-timing a saucer pass from the bumper position by Cooley.
Zetterlund put the Sharks back in front 3-2 at 5:00 of the third period, finishing a cross-crease pass from Nikolai Kovalenko for a power-play goal.
"[We have to] be on our toes, win 50-50 [battles and] play through people," Zetterlund said. "All the simple stuff, but we have to do it every day."