Marchessault said he thinks Kolesar's goal changed the game for the Golden Knights.
"I think we really hit our stride when [Kolesar] scored that goal," he said. "It was a great shot from him."
Kolesar said, "I'm sure I surprised the whole world with that one. Just found some space and wanted to get the puck on net before he could react. Luckily it found its way in the back of the net."
Marchessault scored in front 46 seconds later to extend the lead to 3-1 at 4:04. Vegas won the puck back in the corner, and Marchessault got a piece of Barbashev's shot from the left circle.
"We've got to pick up from that point and press on," Laviolette said. "I think we lost our way a little bit after that."
Marchessault scored again at 2:11 of the third period to make it 4-1.
Kaapo Kakko cut it to 4-2 at 18:54 when he scored off a rebound.
Marchessault scored an empty-net goal at 19:30 for the 5-2 final.
New York outshot Vegas 39-20 and had a 79-42 advantage in shot attempts.
"Right now, what we're doing offensively is missing, is not connecting," Laviolette said. "The opposition is connecting with the scoring chances that we're giving up. Everything is almost two to one. We're in that spot right now, so at the end of the day we're losing games and it's not good enough. You've got to dig in somehow and be better in all areas. Better defensively. More determined offensively. Find a way to win hockey games."
NOTES: Rangers defenseman Ryan Lindgren (upper body) left the game with 11:51 remaining in the first after a hit from Kolesar. There was no update. … Golden Knights forward Pavel Dorofeyev (upper body) didn't play in the third period. It's not clear if he will be able to play Saturday. … Cassidy said forward Michael Amadio has been cleared and should play against the Red Wings. Amadio has missed five games with an upper-body injury.