After Jack Eichel outraced Jackson LaCombe to get an icing waved off, Pavel Dorofeyev was able to skate into the loose puck along the right boards. Dorofeyev then skated through two Ducks defenders and sent a cross-crease backhand pass to Barbashev, who buried the puck into the open net at the left post.
Mitch Marner scored an empty-net goal at 19:54 for the 3-1 final.
Game 2 of the best-of-7 series will be here on Wednesday (9:30 p.m. ET; HBO MAX, truTV, TNT, SN360, SN, TVAS).
Brett Howden scored for the fourth straight game, and Carter Hart made 33 saves for the Golden Knights, who are the No. 1 seed from the Pacific Division.
Mikael Granlund scored, and Lukas Dostal made 19 saves for the Ducks, who are the No. 3 seed from the Pacific.
Howden put Vegas ahead 1-0 at 3:14 of the second period. Marner sent a backdoor pass to a driving Howden, who tapped it into an open net at the left post.
LaCombe passed up an opportunity to tie it at 7:05 of the second period. Leo Carlsson spun around Golden Knights defenseman Noah Hanifin before finding LaCombe, who attempted to bump it to Troy Terry instead of shooting at a wide-open net.
Granlund did tie the game 1-1 at 13:57 of the third period. LaCombe's drive to the net was stopped by the left pad of Hart, but the rebound kicked out to Granlund, who scored through the legs of Brayden McNabb.
However, Vegas was able to regain the lead just 65 seconds later.
