Colton Sissons had a goal and an assist, and Ivan Barbashev also scored for the Golden Knights, who are the No. 1 seed from the Pacific Division. Carter Hart made 31 saves.
Logan Cooley and Kevin Stenlund scored, and Karel Vejmelka made 27 saves for the Mammoth, who are the first wild card from the West and were playing in the first Stanley Cup Playoff game in franchise history.
Game 2 of the best-of-7 series will be here on Tuesday (9:30 p.m. ET; Utah16, SCRIPPS, ESPN2, TVAS2, SN, CBC).
Stone tied the game 2-2 on a power play at 5:33 of the third period. Vejmelka made the first save on Tomas Hertl’s redirection at the edge of the crease, but Stone jumped on the rebound and buried the puck into the open net.
Dowd then gave Vegas a 3-2 lead at 7:20, redirecting Noah Hanifin’s shot-pass over Vejmelka's left pad from the slot.
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 after his initial attempt hit the post.
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 the right boards. Hart got back in time to make the save, but the rebound deflected in off Golden Knights defenseman Kaedan Korczak.
