Jacob Trouba had two goals and an assist, Mika Zibanejad had three assists to extend his point streak to eight games, and Igor Shesterkin made 26 saves for the Rangers (27-11-4), who trailed 3-1 in the second period after they were outshot 16-4 in the first period.
Trouba said the slow start could be attributed to their late arrival home after losing 6-3 at the Carolina Hurricanes on Friday. Bad weather delayed their return flight, and they didn't get in until after 4 a.m. ET.
"Wild 48 hours for us," Trouba said. "It took a little bit to get our legs and our momentum going, but we had good composure in between periods. We didn't like our game. We stuck with it. We know we have a team that is capable of turning it on. You don't want to rely on turning it on and off, but a unique 48 hours for us and it's good to be able to do that."
Clayton Keller, Andrew Ladd and Liam O'Brien scored for the Coyotes (10-26-4), who have lost two in row after winning two straight.
Karel Vejmelka allowed six goals on 20 shots before being replaced by Scott Wedgewood after Trouba's second goal gave New York a 6-3 lead at 1:33 of the third period. Wedgewood made six saves.
"There's two parts, the first part really good and the second part not at all," Arizona coach Andre Tourigny said. "It's not like as a team we're used to that. We fought in every game since the beginning of the season. … We're happy about the consistency of our effort since the beginning of the season. We're not tonight. We'll address it on Monday."
The Rangers comeback started with Kreider's shorthanded goal at 11:30 of the second period that made it 3-2.
"That was the biggest thing, definitely," Gallant said. "The shorthanded goal was huge for us. It was a big, big goal. It got us back to 3-2. It was definitely the momentum changer."
Julien Gauthier scored from the slot at 15:26 to tie it 3-3. The forward was a late addition to the lineup, replacing Kaapo Kakko, who was scratched with an upper-body injury after skating in warmups.
Artemi Panarin scored a power-play goal to give New York a 4-3 lead at 16:33, and Kreider's second of the game made it 5-3 at 18:42.
Kreider's power-play goal at 10:06 gave him the hat trick and made it 7-3.
"We started the second period well, we had our chances, we give that goal on the PK and then the game turned around," Tourigny said. "From there I did not like the way we fought. The grit we had was not there. That's the part we're sour about."