Josh Doan put the Coyotes ahead 1-0 at 5:20, picking up the rebound off a one-timer from the right face-off dot by Jack McBain and sending it past the stick of Pickard.
Henrique tied it 1-1 at 1:49 of the second period, taking a centering pass in front of the net from Kane and sliding it between the legs of Vejmelka.
“These games can kind of at times go under the radar as everybody talks about tomorrow,” Henrique said. “I thought we did a good job of focusing on what we needed to do, but we didn’t have the best start.
“I thought we battled and had opportunities, but we couldn’t find a way to get that next one to give us that extra momentum.”
Logan Cooley gave Arizona a 2-1 lead at 5:37, swatting the rebound of a Sean Durzi shot in off the pads of Pickard.
Nurse tied it 2-2 at 1:12 of the third period with a point shot off a bank pass from behind the net by Warren Foegele that got past a screened Vejmelka.
“They’re a young team with a lot of guys trying to establish themselves in the League,” Kane said of the Coyotes. “And when you have a lot of players like that, they don’t really care where they are in the standings or how many games are left, they’re looking to bring their best every night, playing with nothing to lose.”