The five-goal outburst tied the Red Wings' season high for a game and it was their most since collecting that many against Nashville on Oct. 21. It also was Green's fourth of the season, and his first since he had a hat trick against Ottawa on Oct. 17.
It also gave Detroit its second straight win after losing four in a row. The Red Wings opened the season with a 6-2 record and were 2-8-1 before winning the last two.
"This win a confidence booster, yes," Green said. "It's something to build on for sure and we just have to continue this and it's definitely a positive thing for us to move forward on for sure."
The Red Wings started the overtime on a power play and the game ended with the teams playing 4-on-4 because the clock never stopped during the extra session.
Nielsen made the big play by making a cross-ice pass from the left circle to Green in the right. The defenseman waited a second and then fired that puck past defenseman Andy Greene and beat Cory Schneider, who faced 33 shots.
"I just saw Nielsen had a little bit of time there and he made a great play," Green said. "I just had to get around their first guy in close so I just had to hit the net to try and create something."
Dylan Larkin and Anthony Mantha also scored for the Red Wings, who lost goalie Jimmy Howard to a lower-body injury in the first period. Petr Mrazek finished and allowed three goals on 13 shots in relief.
John Moore, Mike Cammalleri, Pavel Zacha and Adam Henrique scored for the Devils (7-0-2). They have not lost at home in regulation this season.
"Points are important so the fact that we got a point out of the game is certainly is a positive," Devils coach John Hynes said. "How we played the game is not how we wanted to play and I think we were fortunate to be able to get a point out of the game. We need to be much better tomorrow."
The Devils it at 4 with 5:11 left in regulation when Henrique tipped a point shot by former Red Wing Kyle Quincey into the net with New Jersey having an extra skater with a delayed penalty about to be called.
Mantha had given the Red Wings the lead with a blast from the left dot 43 seconds into the third period.
Nielsen gave the Red Wings took a 2-1 lead after the first period. New Jersey went ahead 3-2 in the second period on a goal by Cammalleri and a power-play tally by Larkin with 1.2 seconds left in the period.
The Devils challenged the goal, saying that Gustav Nyquist was offside. After a review, Larkin's sixth goal stood.
John Moore gave New Jersey an early 1-0 lead and the Devils looked in good shape after Riley Sheahan was assessed a four-minute minor for high sticking.
Abdelkader stripped the puck from Damon Severson, took a shot and Nielsen put in the rebound with Schneider down in the crease.
Shortly after coming out of the penalty box, Sheahan took a shot between the circled and Nielsen again put in the rebound with a little help from Devils forward Kyle Palmieri, who seemed to nudge the puck over the goal line.
Cammalleri, who has six points in two games back in the lineup, got his goal on a shot that deflected off the skate of Red Wings defenseman Jonathan Ericsson at 4:06 of the second period. Zacha scored less than two minute later on a shot from the left circle.
NOTES: Abdelkader had the best save of the game with a skate stop on Cammalleri with Mrazek out of position in the second period. New Jersey was leading 3-2. ... Nielsen has 10 goals in 45 games against the Devils. ... Palmieri returned to the Devils' lineup after missing two games with upper body soreness and played in his 100th game with New Jersey.