Puempel scored 2:24 into the game for a 1-0 edge and New York built a 3-1 lead over the next 20 minutes. Arizona rallied to tie it on Tobias Rieder’s goal 7:32 into the third, but then Puempel made it 4-3 with a power-play score with 5:20 remaining.
After a goal by J.T. Miller with 26.7 seconds left made it 5-3, Puempel completed his hat trick with 16.7 seconds to go by redirecting a pass from Brandon Pirri.
Nick Holden also scored on a power play and Chris Kreider added an even-strength goal for the Rangers. Antti Raanta made 18 saves.
Christian Dvorak and Anthony Duclair helped rally the Coyotes with goals, but Mike Smith stopped just 26 of 31 shots.