Filip Chytil put New York ahead 3-1 at 14:20 of the third period, scoring in his third straight game. He knifed down the middle, lost the puck twice but found it both times. From below the left circle, Chytil winged the puck to the net with his backhand and it knocked in off Shea Theodore's left skate.
Jimmy Vesey scored an empty-net goal from the far circle at 18:37 for the 4-1 final.
The Rangers are 16-4-3 since Dec. 5. They won't play their next game until Feb. 6 following the NHL All-Star break.
"We really turned it around and a big credit to everyone in here," New York center Mika Zibanejad said. "We believed in this group. We believed in each other. We knew what we had to do. We weren't happy the way we were playing the first 25 games or so, but everyone was just trying to get back to what we did well last year, trying to understand to do the simple things, the little details that really matter.
"We know that's when we're a good team, when we pay attention to those little details and work together. That's what we've been seeing."
The Golden Knights began the season 16-4-1 and had scored the first goal in 14 of their 21 games. They are 13-14-2 since and have allowed the first goal in 18 of 29, going 4-12-2 in those games, including Friday.
"You've got to show that you're involved physically, that you're desperate to win the hockey game," Vegas forward Jonathan Marchessault said, "and I think we don't have that desperation right now."
The Golden Knights play at the New York Islanders on Saturday, their last game until Feb. 7.
"I think everybody needs to look at themselves in the mirror, maybe look at their game," Marchessault said. "I think we've got to play a little more inside. Sometimes goals aren't always the prettiest, but they still count. I think we've got to get inside.
"Everybody, it doesn't matter who it is or who you're playing with, if it's your turn to get inside or drive the net or get in front of the net you've got to do it. We need more of a mentality of just a grind. Winning hurts sometimes and we've got to find a way."
NOTES: Theodore played 22:14 and was minus-3 in his first game since Dec. 9; he missed 20 straight games with a lower-body injury. … Vegas forward William Carrier had an assist in his return after missing five games with an upper-body injury. … Kreider is the sixth player in Rangers history with eight or more 20-goal seasons, joining Rod Gilbert (12), Jean Ratelle (nine), Adam Graves (eight), Andy Bathgate (eight) and Camille Henry (eight).