WATCH: [All Golden Knights vs. Coyotes highlights]
With goalie Marc-Andre Fleury pulled, Vegas defenseman Nate Schmidt scored on the rebound of a Neal shot to tie the game 1-1 with 1:12 left in the third period.
"Yesterday was honestly one of the best feelings I've had in hockey, and we said we wanted to follow it up again today and get a big win and go home a happy team," Neal said. "We were pushing. We were right there, I thought. From the second period on, I thought we were taking the play to them."
Neal scored his third goal when he skated out in front from behind the net after receiving a pass from David Perron. Schmidt had the second assist.
Antti Raanta made 42 saves in his Arizona debut, 19 in the second period, including a breakaway against Jonathan Marchessault and a post-to-post stop on Erik Haula.
"He was great," Coyotes coach Rick Tocchet said. "He kept us in the game for some stretches in the second. I don't think they had a ton of [Grade A chances], but I know when they did, Antti was superb."
Tobias Rieder scored at 5:52 of the first period to give the Coyotes a 1-0 lead. Arizona (0-1-1) cycled the puck deep in the Vegas zone before pushing it back to Luke Schenn at the point. Schenn moved laterally at the blue line to get the puck through to the slot, and forward Jordan Martinook swept it to Rieder at the far post for an easy tap-in.