Ryan Nugent-Hopkins had his first two points of the season with a goal and an assist, and Cam Talbot made 23 saves for his first win. It was Talbot's first win against the Rangers, who traded him to the Oilers on June 27, 2015. Talbot was previously 0-4-0 against New York.
"These two games are always circled on the calendar for me," Talbot said, "so now I got this one out of the way, it can just go back to being another game."
Henrik Lundqvist made 25 saves, and Mika Zibanejad scored for the Rangers (1-4-0), who couldn't build on their come-from-behind 3-2 overtime win against the San Jose Sharks on Thursday.
"We improved a lot of things we wanted to improve; it came down to discipline," Lundqvist said. "We took too many penalties [four], and in the end, they won the game on that."
The Oilers felt better about the way they played defensively than they did in their first two games, when they allowed three against their penalty kill and were outshot 59-45 in losses to the New Jersey Devils and Boston Bruins.
They were 2-for-2 on the penalty kill Saturday and held the Rangers to 24 shots on goal.
"Our whole defensive game was just a lot better," Nugent-Hopkins said. "Just the way that we checked, we were more of a five-man unit. If there was a little breakdown, it wasn't a huge breakdown where they're getting a quality, quality chance."
McDavid's power-play goal gave the Oilers a 2-1 lead at 6:23 of the third period. His backhand looked like it was going to go through the crease until it went in off Lundqvist.
"He had a little time so he kind of froze me, and I tried to get my pad across and my stick there, but the puck found a way in, through my arm or something," Lundqvist said.
Zibanejad's first goal of the season gave the Rangers a 1-0 lead at 12:49 of the first period. Marc Staal's pass from the left circle deflected off Oilers defenseman Adam Larsson to Zibanejad, who scored from the bottom of the right circle.
Zibanejad had a shot hit the left post at 3:57 of the first period and another at 17:33 of the second period.
"We have to have more a tenacity in the offensive zone," Rangers coach David Quinn said. "Just because it appears someone might defend you, you have to earn your ice, you can't just concede he's going to defend you. We've got to shoot more."
Nugent-Hopkins made it 1-1 with his first point of the season at 14:17 of the first.