Jack Hughes and Chris Tierney scored for the Devils (37-36-5), who have lost four of five (1-3-1). Kaapo Kahkonen allowed one goal on five shots before leaving with an injury in the first period. Jake Allen made 29 saves in relief.
"It's a good hockey team over there. They work," Allen said. "They don't have the most overly skilled lineup, but everyone contributes every night and that's why they're in the playoff (hunt) right now. Good teams are going to do that ... they're going to get momentum. It's how you manage that momentum and create your own."
New Jersey is five points behind the Detroit Red Wings for the second wild card from the Eastern Conference.
"To lose a game in the shootout, I just close my eyes and hope to hear the crowd roar," New Jersey coach Travis Green said. "It's a lot more fun when you win."
O'Reilly scored the only goal in the second round of the shootout. Saros denied Timo Meier, Jesper Bratt and Hughes.
"It's weird, obviously, for the amount of time I played with Allen (with the St. Louis Blues). ... He kind of knows my normal moves," O'Reilly said. "So, I kind of thought I'd do something a little different on him and just try to see what I could get. Lucky for me it got past him."