Jonathan Marchessault scored, and Logan Thompson made 32 saves for Vegas (19-8-1), who have lost three consecutive home games.
"It's not the end of the world, we got a lot of hockey left," Vegas coach Bruce Cassidy said. "We put ourselves in a good position after the second period to get back into the game, then we mismanaged the puck, then it snowballs. It was an issue all game. We got away with it in the first period, get better in the second. We weren't very good at managing the puck in the third.."
Zibanejad gave the Rangers a 2-1 lead with a power-play goal at 5:59 of the third period, one-timing a pass from Panarin. It was Panarin's 600th NHL point.
Filip Chytil made it 3-1 just 24 seconds later at 6:23 on a Barclay Goodrow pass on the rush.
Alexis Lafreniere
made it 4-1 at 7:52 when he shot above a sprawled-out Thompson, who had lost his stick.
Zibnejad capped off the four-goal stretch with another power-play goal, one-timing another Panarin pass at 11:34 from the left face-off circle.
"Our power play got us going in the third and like I said, I just think it was a good solid game right through," Gallant said. "But you know those games when you play well, sometimes you lose them and that's always in the back of your mind too."