O'Reilly shuffled the puck several times before sending a shot beyond the glove of Devils goaltender Jake Allen.
Roman Josi scored in the first period and Luke Evangelista scored the game-tying power-play goal in the third for the Predators, who won for just the second time in six games but snapped a tie with the Vegas Golden Knights for the first wild-card spot in the Western Conference.
Nashville is seven points ahead of St. Louis and will clinch a playoff berth with one more point or one more loss by the Blues.
Jack Hughes and Chris Tierney scored for the Devils, who are five points behind the Detroit Red Wings in the race for the second Eastern Conference wild-card berth but have three other teams between them.
Allen recorded 29 saves in relief of Kaapo Kahkonen, who was injured while trying to stop Josi's goal. See a match summary here.
Blues 6 Ducks 5 (SO)
Jordan Kyrou earned three assists and scored the lone goal in the shootout as visiting St. Louis edged Anaheim.
Robert Thomas had a goal and three assists for the Blues, who have earned at least one point in seven of their past nine games. Zack Bolduc, Matthew Kessel, Pavel Buchnevich and Brayden Schenn also scored for St. Louis. Jordan Binnington made 33 saves, then blanked the Ducks in the shootout.
Frank Vatrano and Leo Carlsson each scored twice for Anaheim, which has won just two of its past 16 games.
Rangers 5 Canadiens 2
Chris Kreider scored a tiebreaking power-play goal 3:59 into the third period, Artemi Panarin added a goal and three assists and host New York defeated Montreal thanks to a four-goal third period.
The Rangers matched the franchise record for regular-season wins set in 2014-15 (53) and won for the eighth time in nine games (8-1-0). Mika Zibanejad finished with two goals and an assist and Alexis Lafreniere added an empty-netter. Igor Shesterkin made 26 saves.
Cole Caufield and Alex Newhook scored Montreal's goals, and Mike Matheson assisted on both. Cayden Primeau made 41 saves for the Canadiens.
Red Wings 3 Sabres 1
Lucas Raymond had a goal and an assist for Detroit in a win against visiting Buffalo.
It was the 40th multi-point game of Raymond's career, making the forward the eighth Red Wings player aged 22 or younger to reach that mark. Patrick Kane and Dylan Larkin scored for the Red Wings, who jumped into the second wild card in the Eastern Conference. Alex Lyon made 37 saves.
Tage Thompson scored and Ukko-Pekka Luukkonen made 21 saves for the Sabres, who dropped five points behind the final playoff spot with four games remaining.
Wild 4 Blackhawks 0
Kirill Kaprizov had two goals and an assist and Jesper Wallstedt made 24 saves for his first career victory and shutout as visiting Minnesota defeated Chicago.
Minnesota moved within nine points of the Golden Knights for the final Western Conference wild-card spot with five games remaining. Wallstedt kept the Wild's flickering postseason aspirations intact with a bounce-back effort from his NHL debut, a 7-2 loss at Dallas on January 10th.
Recently recalled from Minnesota's AHL affiliate in Iowa, Wallstedt shut down a Blackhawks team that had struck for 16 goals in its past four victories. Chicago couldn't slow Minnesota's hottest player nor generate much of an attack.
Hurricanes 3 Blue Jackets 0
Andrei Svechnikov and Sebastian Aho scored in the first period to set the tone and Carolina rode another shutout from Frederik Andersen to win its regular-season home finale, defeating Columbus in Raleigh, N.C.
Teuvo Teravainen tacked on a third-period goal after providing a first-period assist. Andersen posted his third shutout in his past seven outings, needing 23 saves. It was Andersen's 27th career shutout.
Goalie Malcolm Subban made 32 saves in his first NHL game of the season for the Blue Jackets, who had won three of their previous four games.
Coyotes 5 Sharks 2
Clayton Keller, Lawson Crouse and Nick Schmaltz each recorded a goal and an assist as Arizona swept the season series with host San Jose.
Liam O'Brien and Dylan Guenther had the other Coyotes goals, while Connor Ingram made 25 saves. Arizona has won seven of its past 11 games (7-4-0).
Henry Thrun scored a goal and assisted on Luke Kunin's marker for San Jose. Mackenzie Blackwood stopped 23 shots for the Sharks, who have lost 11 of their past 14 (2-11-1).
Senators 3 Capitals 2 (OT)
Jake Sanderson scored 41 seconds into overtime to lift Ottawa to a win over host Washington.
Sanderson's 10th goal of the season capped a comeback for Ottawa, which trailed midway through the third period before Ridly Greig scored to force overtime. Mark Kastelic also scored for the Senators, who got 20 saves from Joonas Korpisalo.
Max Pacioretty and Aliaksei Protas scored for Washington, while Charlie Lindgren had 18 saves. The Capitals collected one point for reaching overtime but missed out on a chance to gain two while being bunched up among the teams within a point of the second wild-card berth in the Eastern Conference.
Stars 7 Avalanche 4
Wyatt Johnston and Jamie Benn each had a goal and two assists, Tyler Seguin scored twice and Dallas beat Colorado in a critical Central Division matchup in Denver.
Matt Duchene had a goal and an assist and Roope Hintz and Mason Marchment also had goals for travel-weary Dallas, which moved closer to clinching the division crown with its ninth win in 10 games. Jake Oettinger turned away 34 shots.
Jonathan Drouin, Sean Walker, Artturi Lehkonen and Brandon Duhaime had goals, Nathan MacKinnon added two assists and Alexandar Georgiev made 30 saves for the Avalanche.
