Nash scored what turned out to be the game winner when defenseman Brady Skjei found him darting toward the back post at 18 minutes 53 seconds of the second period. McDonagh also assisted on the play.
“We kind of talked about that play before the game, and we knew there’s going to be a chance it would be open,” Nash said of his power-play goal against Oilers goaltender Cam Talbot. “Brady and I talked about it, and he made a great pass. You just try to build a wall with your skates and your sticks, and you hope it hits something. When you get a goalie like Cam, we know him pretty well. He challenges hard. He leaves that backdoor play open.”
New York had jumped in front, 1-0, when Nash and Kevin Hayes completed an odd-man rush at 12:16 of the first period. Zuccarello also assisted on the play.
“I just look to see what stick the defenseman has. When it’s a lefty on lefty, you just wait for him to move his stick,” Hayes said of the two-on-one opportunity. “You just got to wait out the goalie, then make your decision from there.”
Puljujarvi, playing in his first game of the season since being called up Friday from the A.H.L., tied the game with a wrist shot at 16:26 of the first period. Skjei and Buchnevich each had difficulty clearing the puck from the defensive zone, and eventually Ryan Nugent-Hopkins controlled it. He delivered a soft backhanded pass to Puljujarvi before the wrist shot. Darnell Nurse also assisted on the play.
McDavid added a power-play goal in the middle period, extending his point streak to three games.
“They were able to get two quick ones on the power play,” Oilers coach Todd McLellan said. “They do such a good job in the neutral zone of clogging things up that it’s hard to come back against them.”
Buchnevich scored for the third time in three games when Shattenkirk delivered a cross-ice pass to set up the one-timer at 15:10 of the second period. Since Oct. 26, Buchnevich has the N.H.L. in goals, with seven.
Michael Grabner added an empty-net goal with 1.4 seconds remaining.
Talbot made 30 saves for Edmonton.
The Rangers, who had a disappointing 3-7-2 start this season, can look to a third-period rally on Oct. 31 against the expansion Vegas Golden Knights as a turning point in their season. The Rangers trailed, 4-2, at the end of the second period and scored four unanswered goals to begin their winning streak.
“The things we want to do have stayed the same,” Rangers Coach Alain Vigneault said. “There’s no doubt that we’re executing better. With that execution, it doesn’t lead to costly mistakes, and we’ve been able to build off that the last few games and play, for the most part, pretty good hockey.”
There was a scary moment at 3:24 of the second period, when Edmonton’s Zack Kassian and the Rangers’ Jimmy Vesey got tangled up. As both fell to the ground, Kassian’s skate clipped Vesey in the mouth. Vesey returned with full cage to start third period.