Nash opened the scoring 12:19 into the game on a 2-on-1 break with Kevin Hayes, who fed Nash for the one-timer. Nash now has five goals in his last four games.
Edmonton scored the next two, beginning with Jesse Puljujarvi's first goal of the season at 16:26 of the first before McDavid's power play tally in the second.
Michael Grabner scored an empty-net goal with 1.4 seconds remaining.
The power play has been a catalyst for the team's rebound following a tough start to the season, especially during this current win streak. The Rangers have power play goals in five of their last seven games, doing 9-for-23 during that stretch.
"It's definitely made a big difference for us," said Shattenkirk, who is tied for first among defensemen with nine power play points. "We've had a few games here where it's helped us get back in the game and take the lead. More than anything, we've gotten momentum off it no matter what, and I think that's our focus every time we get out there."
It was nearly two weeks ago that New York was 3-7-2 out of the gate. Now, they're tied with New Jersey and Pittsburgh for the most points in the Metropolitan Division.
"I think we'd been playing some pretty good hockey for quite some time. Our record in the last 10 games is very good. Probably one of the best in the NHL right now," coach Alain Vigneault said. "We're working on our game; we're working on putting a complete game on the ice. There's no doubt that this group is very resilient, very hard-working and we're just trying to get better."