"I don't think many people would have thought he'd get 20 wins in the NHL this season, that's for sure," Langenbrunner said.
Patrik Elias scored his 21st goal in the first as the Devils recorded their sixth straight victory, the team's longest winning streak of the season.
Clemmensen, who made 21 saves, returned to the Devils organization as a free agent during the offseason and came up from the minors to wrestle away the starting job from backup Kevin Weekes after four-time Vezina Trophy winner Martin Brodeur was lost to elbow surgery in November.
"My previous high coming into this year was three," said Clemmensen, who improved to 20-9-1 overall this season. "It feels good. Why stop at 20? There's more to go and you take it one game at a time and hopefully 20 can become 21, and then 22, 23 and so on, so forth."
Clemmensen had three wins with New Jersey in 2003-04 and again in 2005-06. He had an overall NHL record of 8-7-4 in 28 games prior to this season, including a win and a loss in three games last season with Toronto.
Alexandre Picard scored a power-play goal in the second for Ottawa, which had recorded points in each of its four previous games (3-0-1).
New Jersey had a five-game streak from Nov. 15-26 and a four-game run from Dec. 4-12.
Langenbrunner scored in the second to restore the Devils' one-goal lead before adding his second goal of the game 19 seconds into the third to make it 3-1.
Senators right winger Chris Neil and New Jersey's David Clarkson had a lengthy fight just two minutes before Shanahan, who scored in his return with the Devils in a 3-1 win in Nashville on Jan. 19, got a double-minor for high sticking at 5:42.
"We didn't generate enough off that power play," Ottawa center Jason Spezza said. "It was a chance for us to score and get back in the game and we were a little bit sloppy with our execution."
The Senators failed to record a shot as New Jersey successfully killed the four-minute penalty and Shanahan made it a three-goal margin when he put a snap shot past Brian Elliott at 11:17.
"He's scored 600 and some goals in this league because he knows what to do with the puck in the offensive zone, and that was a perfect shot," Devils coach Brent Sutter said. "The two goals he's scored are goal-scoring goals, that's what a goal scorer does."
Elliott stopped 23 shots in his sixth straight start for the Senators.
"It's obviously what you want, you want to be in that position, but you can't have games like that as a team," said Elliott, who has started every game since he was called up from AHL Binghamton on Jan. 9. "I have to work my hardest to stay where I am and I'm going to continue to do that."
Elias opened the scoring 4:54 in as New Jersey held an 11-8 margin in the opening period and 27-22 overall.
Picard drew Ottawa even at 1 with his sixth goal midway through the second.
Langenbrunner banked in a shot off Elliott at 14:19 as the Devils regained the lead.
The Devils captain extended the lead to 3-1 when he scored early in the third.
It was Langenbrunner's 17th career two-goal game. He has yet to record an NHL hat trick. ... Each of Picard's six goals this season have been scored on the power play.