Johnny Brodzinski, Braden Schneider and Taylor Raddysh also scored for the Rangers (5-5-2), who improved to 5-1-1 on the road.
Darnell Nurse had a pair of goals and Matt Savoie had his first career goal for the Oilers (5-4-3), who have lost three of their last four.
Igor Shesterkin registered 33 saves to collect the win for the Rangers, while Stuart Skinner made 30 stops for the Oilers.
Rangers: Before earning the late overtime win Shesterkin had his struggles against Edmonton. He came into the contest with a 1-3 record, an .886 save percentage and 3.00 goals-against average versus the Oilers. In 230 starts against the rest of the league, he had posted a .918 save percentage and 2.47 GAA.
Oilers: Forward Adam Henrique, who picked up an assist, received his silver stick for playing 1,000 regular season NHL games in a ceremony before the contest, having achieved the feat just over a week ago in a game in Ottawa, when he became the 409th player in NHL history to do so. Remarkably, he is the first player to have ever hit 1,000 game as a member of the Oilers.
The Oilers got a bizarre one to take a 3-1 lead midway through the second frame as Nurse took a shot from a bad angle near the goal line that nobody initially thought went in until a review during a TV timeout determined that the puck was sitting on top of Shesterkinâ€s pads as he backed into the net.
The Rangers are still the only team in the NHL without a single forward who had reached eight points this season, being led by defenceman Adam Fox with nine points. Artemi Panarin leads the forwards with seven points.
Rangers: Complete a four-game trip in Seattle against the Kraken on Saturday.
Oilers: Host the Chicago Blackhawks on Saturday.
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