Montreal unsuccessfully challenged Zibanejad's goal for goaltender interference, resulting in a Rangers power play. Kreider scored on it, making it 4-1 with a deflection in front at 15:19 and ending New York's 0-for-18 slump on the power play.
"After the first period it was Mika and 'Kreids' and 'Foxy' picked it up, Panarin," New York coach Peter Laviolette said. "Our big guys got going and started really playing a much better game on the attack. … There were good things after the first period."
Slafkovsky scored with a wrist shot from the slot after a Rangers turnover to make it 4-2 at 16:30.
Vincent Trocheck extended the lead to 5-2 at 4:23 of the third with a snap shot from the high slot off a drop pass from Panarin.
Caufield cut it to 5-3 on the power play at 6:53. He redirected a shot from Mike Matheson in front that missed the net, went off the end boards and in off Quick's skate.
Kreider completed his hat trick by scoring off a 2-on-1 with Zibanejad to make it 6-3 at 7:59.
Kaapo Kakko picked up the puck at the right-side boards, cut through the right circle and beat Montembeault from a tight angle to push it to 7-3 at 9:56.
Caufield scored his second with a wrist shot between the circles at 11:27 for the 7-4 final.
"We've been finding ways to win differently," Zibanejad said. "I think we've played way better. There's been a few periods when we're not happy, but overall, it's been trending in the right direction. We've just got to keep it going."
NOTES: Gallagher played 12:24 in his return from a five-game suspension for an illegal check to the head of Islanders defenseman Adam Pelech on Jan. 25. … Slafkovsky has 11 points (six goals, five assists) during his point streak. ... Rangers forward Blake Wheeler left the game with a lower-body injury at 10:47 of the first period. Wheeler couldn't put weight on his right leg as he was helped off the ice. He had to be put on a stretcher to be taken down the tunnel toward the dressing room. There was no update. He'll be evaluated Friday. … The Rangers tied their longest winning streak of the season (Oct. 21-Nov. 2).