O'Reilly's team-leading 21st goal of the season came off a quick release from the slot after he collected a pass from Matt Duchene, giving the Avalanche their first power-play goal in five opportunities against the Devils.
"I was just in front and [the extra attacker] Nate MacKinnon and Tyson Barrie moved the puck well," O'Reilly said. "Dutch [Duchene] just gave me a little tap-in there. I set my stick on the ice and didn't really do too much. I just had it in the right spot."
The Avalanche erased a 1-0 deficit late in the third when coach Patrick Roy pulled goalie Jean-Sebastien Giguere with 2:34 remaining in regulation. PA Parenteau deflected a shot by Tyson Barrie from the right point past Devils goalie Cory Schneider with 1:47 left, marking the third straight game the Devils had allowed the tying goal with less than two minutes remaining in regulation (1-0-2).
"Our guys were playing hard. It was a tight game and sometimes you go with your feeling when to pull the goalie and fortunately it worked for us," Roy said. "I am not going to take any credit for that though. It's the players. We didn't move the puck very well on the power play all game, but we scored the right power-play goal."
Monday marked the beginning of a four-game East Coast swing for the Avalanche (36-14-5) before the Olympic break. They will visit the New York Rangers on Tuesday, Philadelphia Flyers on Thursday and New York Islanders on Saturday.
Colorado has won four in a row and nine of the past 11 games.
"I'm very proud of our group. Every night, the guys are focused and playing hard," Roy said. "That's the reason we had a chance to come back. We gave ourselves a chance to win."
Roy felt the timing was right to pull Giguere.
"We were buzzing and I thought that was the right time; they had the line (Ryan Carter-Stephen Gionta-Steve Bernier) that I thought would be the best for us to score the goal, so why wait?" Roy said. "We might as well know right away, especially when you're putting on that pressure."
After tying the game, Colorado was given its fifth power-play of the game after Devils forward Michael Ryder made an ill-advised, no-look pass in his own end that Duchene intercepted and broke in over the Devils blue line before defenseman Andy Greene took a slashing penalty at 19:18. The penalty carried over into the overtime, giving Colorado a 4-on-3 advantage.
"It's frustrating but that's what we're dealing with right now," DeBoer said. "Giving up a lead late in the game wasn't an issue all year, but it has been the past three games.
"Tonight, the story is we have to find a way to get the second and third goal; we got one goal out of our fourth line and enough chances to get five. If you let anybody hang around in this League long enough, bad things will happen and that's the story lately."
The Devils rang the post three times in the game; two off the stick of Dainius Zubrus.
Giguere, who was making his first start since Jan. 6, made 27 saves. It was Giguere's first win since Dec. 6, a 3-2 victory against the Calgary Flames.
"You always want to be positive and think about getting the win," Giguere said. "When we did tie it up, what goes through your mind is winning. It's about getting the next goal and our guys showed character. It was a frustrating game because the Devils were playing really well. There wasn't much room out there. But we showed resiliency and found a way to get two big goals in the end."
Schneider (10-11-8), who was making his fourth straight start and sixth in the past seven games, made 23 saves. He entered the game second in the NHL with a 1.91 goals-against average and was tied for fifth with a .925 save percentage.
"Cory deserved the win," DeBoer said. "It sounds like a broken record. I'm not questioning our effort because it's there, but we need to score that second and third goal."
Jaromir Jagr barely missed at giving the Devils a 2-0 advantage early in the third when his shot rolled up and over the left pad of Giguere and stopped on the goal line behind his left skate at 4:06. A video review confirmed that the puck did not completely cross the line.
The Devils (23-22-12) outshot the Avalanche 11-6 in the first and also hit two posts. Carter's fifth goal of the season off a slap shot from the left circle gave New Jersey a 1-0 lead. The goal, which beat Giguere just inside the long-side post, came 38 seconds after the Avalanche had successfully killed the Devils' third power-play of the period.
"It's a race to three goals in this League to win a hockey game and we don't get there enough," DeBoer said. "It's not for a effort or generating chances, but we need to finish those. Guys who can score need to score for us."
Schneider's best stop of the first came against MacKinnon when he slid to his left to make a pad save at the right post after an initial shot from the left point went wide and caromed off end boards at 14:51.
MacKinnon, who assisted on O'Reilly's overtime winner, extended his point-scoring streak to five games (three goals, five assists).
Follow Mike Morreale on Twitter: @mikemorrealeNHL