Eric Robinson, Jesperi Kotkaniemi and Jordan Staal each had a goal and an assist, and Jaccob Slavin had two assists for Carolina (11-3-0), which has won nine of its past 10.
It was the seventh straight win for Kochetkov, who is 8-1 with a 2.45 goals-against average.
"‘Kucci’ was great. They had a couple great chances early, and it would have been probably a closer game,” Staal said. “But good goalies find ways to steal a couple and make some big saves for us, and he did that tonight.”
Jack Eichel extended his point streak to three games with a goal and an assist for Vegas (9-4-2), which had its eight-game home winning streak end. Adin Hill gave up four goals on 21 shots before being replaced by Akira Schmid, who made 12 saves
“Some of our veteran guys didn't have the 'A' game in terms of transition and execution. I thought they were fumbling some pucks,” Golden Knights coach Bruce Cassidy said. “So they could have been better and would have needed to be better tonight. But again, I think it was a team loss, to be honest with you.”