Jarkko Ruutu scored for Ottawa. The Senators are 1-4-1 in their last six games.
Gionta and Oduya gave New Jersey a 2-0 lead in the first period.
Gionta scored 40 seconds in, tipping Paul Martin's point shot past Alex Auld.
Early goals have become a Devils' specialty. It was the third straight game in which New Jersey scored in the first 2 minutes, setting a team record.
Oduya scored on a power play at 14:28. Parise had the puck deep in the Ottawa zone when he spotted Oduya charging the net from the left point. Parise threaded a well-timed pass to the onrushing Oduya for the score.
Elias got the second assist on both goals, extending his points streak to nine games. It also was his 169th multipoint game, tying John MacLean's team record.
The Senators, mired in an offensive slump, got a second-period goal from an unlikely source: Ruutu. His short-handed tally at 8:37 was only Ottawa's fifth goal in the last five games. In desperation, Senators coach Craig Hartsburg broke up his big line of Daniel Alfredsson, Jason Spezza and Dany Heatley. It didn't help.
The Devils reclaimed the two-goal lead at 3-1 in the closing seconds of the period when Elias knocked in Parise's rebound for New Jersey's second power-play score.
Zajac scored at 12:09 of the third before Elias' closed it out with his second at 14:39 as the Devils opened a 5-1 lead on their third power-play goal of the game.
Notes: Clemmensen's only previous appearance against the Senators came in relief of Martin Brodeur on Oct. 21, 2006, giving up two goals in an 8-1 loss. ... The Devils lost one and gained one on the blue line. Bryce Salvador missed the game because of an upper-body injury sustained Wednesday in the Devils' 5-3 win in Buffalo. Andy Greene, sidelined since Oct. 29 by a broken right hand, took Salvador's place. John Madden also was scratched. The Devils reported that he was "ill". ... The Ottawa scratches were Jesse Winchester (upper body injury) and Ilya Zubov (an expired travel visa that kept him in Canada). ... Auld was back in goal for Ottawa after Martin Gerber started three of the last four, including the last two. Auld is 0-4-0 against New Jersey.
