"It's pretty amazing," the 27-year-old Greene said. "It feels pretty good to be out there and it's been a lot of fun. I hope we can keep it going."
Patrik Elias and Rob Niedermayer also scored for the Devils, who have won four straight and seven of eight. Martin Brodeur made 21 saves but remained tied with Terry Sawchuk for the most shutouts in NHL history at 103.
Greene scored the second and third goals of the game, giving New Jersey (21-7-1) a 3-0 lead before Carolina scored twice in a span of 1:58 to cut it to 3-2 in the second period.
Greene's recent play has certainly caught the eye of Devils coach Jacques Lemaire.
"We're not an overpowering team offensively, so we need goals from our defensemen," Lemaire said. "I always have a feeling that Andy is going to slow down, but he never does. He plays well every night. It doesn't matter who we're playing against. He's very good. He controls the puck and makes plays. I never thought he could be this good, but right now he's playing like an All-Star."
Brandon Sutter, the son of former Devils coach and current Calgary coach Brent Sutter, had the first goal for the Hurricanes (7-18-5), who dropped to 1-11-3 on the road. Tuomo Ruutu added a power-play goal.
Elias scored the first goal, giving him 299 for his career, and Niedermayer's empty-netter sealed it with 5 seconds left -- ending Carolina's modest two-game winning streak.
"Until the shift where we took the penalty in the third period, I really liked the way we played," Hurricanes coach Paul Maurice said. "We've played well for about a month now. We don't have a whole lot to show for it."
The Devils got a fluke goal in the first. Elias took a pass from Niclas Bernfors and skated in on the right side. His attempted backhand pass back to Bernfors was broken up by Carolina defenseman Aaron Ward, but the puck caromed off Ward's skate and into the net.
Elias' fourth goal of the season came at 11:11.
New Jersey increased the lead to 2-0 late in the period when Greene skated into the Carolina zone untouched and unleashed a rocket slap shot from the blue line.
"From my angle, Andy had very little room to shoot, but it managed to get through," Brodeur said. "It definitely helps when everyone is contributing offensively, because we can't rely on the same guys every game. It helps when you can spread it out, especially among the defensemen."
The shot eluded Carolina goalie Cam Ward, who missed the previous 13 games with a cut on his upper leg that he got from the skate of Columbus' Rick Nash on Nov. 7.
"I felt a little bit uncomfortable at times in the first period, but as the game went along I thought I settled down and played better in the second and the third," Cam Ward said. "By the end of the game, I felt like my normal self."
Early in the second Greene scored again, this time on a power play. With Ray Whitney off for high-sticking, Greene skated into the Hurricanes' zone, got knocked down, but was able to get up in time to knock in a rebound of Zach Parise's shot for his fifth goal of the season.
"I got hit, fell down, and just kept going to the net," Greene said. "The puck came to me and I made the play."
It didn't take long for Carolina to end Brodeur's bid for the record-breaking shutout. Sutter took a shot that skipped and handcuffed Brodeur and found its way into the net just 43 seconds after Greene's second goal.
"It was deflected and then bounced down," Brodeur said. "I was still looking for it when it went past me."
Ruutu scored less than two minutes later.
"We turned the puck over like three or four times in a row in our zone and stopped playing in their zone," Lemaire said. "We tried to be a little too fancy and tried to make plays we were not able to make. They got the momentum going."
The Hurricanes dominated the third period but couldn't score. They had two good shots with two extra men on the ice in the closing minute, but Niedermayer put the game away for New Jersey.
"It's a mentality. We've got to refuse to give up on our season and continue to strive to do better," Cam Ward said.
Devils D Mike Mottau returned to the lineup after missing Monday's game with food poisoning. ... Cam Ward dropped to 2-10-3 this season. ... Brodeur is 28-12-3 against Carolina. He needs three more appearances to tie Patrick Roy for most games played by a goalie in NHL history (1,029). ... Devils D Bryce Salvador went hard headfirst into the boards in the first period and was on the ice for several minutes, but returned to action later in the game. "He wanted to come back," Lemaire said. "At first, I didn't think he would be able to come back, but hockey players are tough."
Copyright by STATS LLC and The Associated Press
Arena: Prudential Center Location: Newark, New Jersey
Referees: David Banfield, Dan Marouelli Linesmen: Michel Cormier, Jean Morin
Attendance: 12,013 (68.2% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Patrik Elias (4)
Assists: Niclas Bergfors, Zach Parise
Andy Greene (4)
Assists: Jamie Langenbrunner, Jay Pandolfo
Andy Greene (5)
(Power Play) Assist: Zach Parise
Brandon Sutter (7)
Assist: Joni Pitkanen
Tuomo Ruutu (7)
(Power Play) Assists: Jussi Jokinen, Joni Pitkanen
Rob Niedermayer (4)
(Shorthanded) (Empty Net) Unassisted