Nick Bjugstad and Zach Hyman also scored for the Oilers, who have won six straight and strengthened their hold on second place in the Pacific Division. Jack Campbell stopped 27 shots.
It is the sixth time in franchise history they have had a points streak of at least 12 games. The last was 2005-06 when they had a team-record, 16-game run.
Nugent-Hopkins, who had the assist on Hyman’s empty-net goal late in the third period, joined Connor McDavid and Leon Draisaitl to reach the century mark this season with the Oilers. The last time a team had three or more players with at least 100 points was Pittsburgh in 1995-96 (Mario Lemieux, Jaromir Jagr and Ron Francis).
McDavid also had an assist on Hyman’s goal to move him within two points of 150.
Troy Terry scored for Anaheim and Lukas Dostal made 30 saves.
The Ducks have dropped nine straight and are 1-10 in their last 11 as they remained tied with Chicago and Columbus for fewest points in the NHL at 56.
It is the third straight season Anaheim has had a winless streak of at least nine games. The loss also guaranteed the Ducks would finish with the fewest points in a full 82-game season in franchise history. The previous low was 65 points in 1997-98, which was the fourth-worst record in the league that season.
Kostin, who was playing in his 100th NHL game, got his first point in 11 games midway through the second period when he took the pass from Mattias Ekholm and put a wrist shot from out front that Dostal was unable to get his glove on for his 11th of the season.
Three minutes later, Kostin made a pass behind the goal to Bjugstad to make it 2-0. It was Bjugstad’s 17th of the season and fourth since he was acquired by the Oilers from the Arizona Coyotes at the trade deadline.
Terry got the Ducks within a goal five minutes into the third on a wrist shot from the left faceoff circle.
Terry — who is tied with Trevor Zegras for the team lead in goals at 22 — had missed Anaheim’s four-game trip due to his wife expecting the couple’s first child.