The Devils lost 8-1 at Scotiabank Place in the teams' first meeting on Oct. 21.
"We thought about it," said Brodeur, who picked up his league-leading 24th win of the season. "You try to step up your game when one of those happens. Revenge was definitely on our minds. We beat them in New Jersey, but it was in this building that we wanted to beat them. We didn't embarrass them, but we won."
Zach Parise also had a goal for the Devils, but it was Brodeur's nearly flawless performance that made the difference. Brodeur stopped 33 shots to prevent the Senators, who had won five of six, from earning at least one point for the first time in seven games.
Gionta's first goal gave New Jersey a first-period lead and his second stood up as the eventual winner.
"I think everyone here was embarrassed (by the October loss)," Gionta said. "It sticks with you. I think everyone wanted to come back here and have a better effort and we did."
Scott Gomez added a pair of assists for New Jersey.
Ray Emery made 26 saves for Ottawa, but the Devils won their second consecutive game and fifth in six tries. Their only loss during that stretch came in a shootout against the New York Rangers.
"That's how they play," Emery said. "They get the leads and try to shut it down. That was kind of the case today."
"(Brodeur) was on top of his game," Eaves said. "They played the typical hockey that they're known to play. We just came up a little bit short."
Both teams are back in action Sunday. Ottawa is at home against Philadelphia, while the Devils play in Montreal.
New Jersey jumped ahead 6:13 into the game when Parise took a pass from Travis Zajac and beat Emery from close range.
The Senators took advantage of a New Jersey turnover to tie the score later in the period. Dean McAmmond stripped David Hale of the puck in Devils zone and Christoph Schubert fed Eaves in the slot. His low shot beat Brodeur for Eaves' first goal since Dec. 2, a stretch of 17 games.
New Jersey killed off a penalty early in the second before Gionta redirected Hale's point shot to restore the Devils' lead.
Brodeur thwarted Senators snipers Dany Heatley and Daniel Alfredsson on several occasions.
Ottawa had a chance for the equalizer with a power play midway through the third, but Brodeur, with Chris Neil repeatedly in his face, stopped Peter Schaefer on a couple of chances.
Gionta made it 3-1 with 3 1/2 minutes left, taking a pass from Gomez in the slot and beating Emery.
Preissing scored from a scramble with 78 seconds left.
- With forwards Mike Fisher (knee), Jason Spezza (knee) and Antoine Vermette (hip) all out with injuries, the Senators recalled center Josh Hennessy from AHL Binghamton for the game.
- Devils D Brian Rafalski appeared in his 500th NHL game.
- C Erik Rasmussen returned to the lineup after being a healthy scratch in five of New Jersey's previous seven games.
- Devils defensemen Colin White and Johnny Oduya (upper body injuries) missed the game.
- D Mark Fraser, from Ottawa, made his NHL debut for New Jersey.