"It seems we find ways to win," Devils goalie Martin Brodeur said. "We stuck with it. It wasn't a really pretty game on our part, but we came through."
The Devils (11-4) are riding the second-longest road winning streak to open an NHL season. The Buffalo Sabres started the 2006-07 season with a 10-game road run.
New Jersey trailed 2-1 heading into the third but scored two power-play goals in the third to pull out the victory.
"This is our team," Devils coach Jacques Lemaire said. "They believe they can come back. It's all tight games that we're getting, but they never let down and they always feel they have a chance to come back."
The Senators (7-5-2) continued their trend of letting games and points slip away because of their mistakes.
"We've just got to find a way to stay out of the box," Senators coach Cory Clouston said. "Whatever it may be, whether we feel we're getting the short end of the stick, we've got to find a way to stay out of the box."
Senators goalie Pascal Leclaire, celebrating his 27th birthday, was angered by his play.
"I'm mad at myself," he said. "I made a mistake on that second goal and then I was screened on the last one. It was frustrating."
The Senators got off to a strong start, but just couldn't hold it together in the final period.
The Senators opened the scoring at 14:00 of the first after creating a flurry of great chances. Daniel Alfredsson found Michalek, who beat Brodeur shortside.
Ottawa made it 2-0 midway through the second on Lee's first goal of the season. Lee carried the puck from his own end and let a wrist shot go that just slipped under Brodeur's left leg. Brodeur sprawled to grab the puck, but it had already trickled across the line.
"Those goals will happen," Brodeur said. "This one was pretty bad, but you've just got to focus on the next one."
The Devils cut the lead in half with a power-play goal as Parise was able to pick the puck out of traffic in front and raise it over Leclaire.
With Jarkko Ruutu serving a holding penalty, the Devils tied it as Clarkson beat Leclaire through the legs from a sharp angle.
"I thought the second goal was the turning point for them," Clouston said. "Obviously it was one that Pascal would have liked to have back, but they were just better positionally than we were. When they got the lead they just shut it down."
Greene scored the eventual winner on a screened shot.
"We played a great start of the game and then took too many penalties again," Ottawa forward Jason Spezza said. "It cost us so it was a frustrating loss."
Senators center Jesse Winchester played his first game of the season after missing the first 13 because of a knee injury.
The Senators have not beaten the Devils since Oct. 27, 2007. ... The Senators were without D Anton Volchenkov (elbow, 2/3 weeks). ... The Devils were missing D Johnny Oduya (lower body, indefinite), C Rob Niedermayer (upper body, indefinite), D Paul Martin, (forearm fracture, four weeks), LW Jay Pandolfo (shoulder, four weeks). ... New Jersey's Patrik Elias was a healthy scratch. Elias returned to the Devils lineup for Friday's home win over the Islanders after missing the first 13 games following groin surgery. He was held out from playing consecutive games for precautionary reasons.
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OTTAWA - NOVEMBER 7: Pascal Leclaire #33 of the Ottawa Senators stands in his crease during warmups prior to a...