Barbashev added an empty-net goal before Vejmelka could get fully off the ice at 18:21 for the 4-2 final.
Cooley gave the Mammoth a 1-0 lead at 19:49 of the first period, one-timing a cross-ice pass from Nate Schmidt past Hart from the right circle.
Sissons tied the game 1-1 at 3:44 of the second period. Brayden McNabb's shot hit Cole Smith in front, and he sent a backhand pass across the crease toward the back post, where Sissons tapped it across the goal line.
“I saw some commotion going on the back side,” Smith said. “I wasn't exactly sure where he was, but this time of year, just throw pucks toward the net and good things can happen.”
Stenlund put Utah back ahead 2-1 at 5:07 of the second. Hart couldn't stop a dump-in from Sean Durzi, and Stenlund quickly put a shot toward the net from along the right boards. Hart got back in time to make the save, but the rebound deflected in off Golden Knights defenseman Kaedan Korczak.
“That was a great game. We know Vegas is a really good team,” Utah coach Andre Tourigny said. “It was a hard-fought game. It was physical. It was intense. Every inch was contested, so I was proud of how we prepped like the way we came out, and I think the guys were pretty composed. They were controlled. When we exploited our speed, it was a good factor for us, so we need to keep focusing on it.”