Panarin scored his second goal at 4:33 of the third period on the rebound of a Braden Schneider shot to give the Rangers a 3-2 lead before scoring glove side on a breakaway at 15:59 to make it 4-2.
After Kaapo Kakko scored an empty-net goal at 17:46 to extend the lead to 5-2, Panarin curled with the puck in the slot and scored on a wrist shot at 18:56 for the 6-2 final.
"Four goals, first time in my life," Panarin said. "If I knew how to explain that, I [would] explain. I don't know what happened tonight, so it's probably my day tonight. Everything [went] in. It's a surprise. Sometimes when I feel something, it's zero points."
Mika Zibanejad also scored, and Vincent Trocheck had two assists for the Rangers (31-14-8), who are 6-0-1 in their past seven games.
"I loved the game. We played a good game against a real good team over there," New York coach Gerard Gallant said. "They're one of the best teams in the NHL. They dump a lot of pucks, they put a lot of pressure on you, and they got some good chances."
Jaroslav Halak made 27 saves in his seventh straight win.
"He was great," Rangers captain Jacob Trouba said. "He made some big saves at key times. He helped the defense a lot stopping pucks behind the net, moving the puck. That's a big help for us. He's been great."