The defenseman scored his first goal of the season with 55.5 seconds left in overtime to give New Jersey a 3-2 victory over the Florida Panthers on Wednesday night, the Devils' fifth consecutive victory.
Oduya scored on a wrist shot that went between Craig Anderson's pads and his glove.
"It found the back of the net, and that's always nice," Oduya said. "I don't score that many goals."
Florida sent the game to overtime with two goals in the last 2:19 of regulation, including David Booth's goal with 7.2 seconds left.
"We were pretty pumped to tie it and we get a power play, and go from thinking that you can end it right there to walking off the ice the other way," Florida center Stephen Weiss said.
Jay Bouwmeester added a goal for Florida.
Florida goalie Tomas Vokoun was pulled in favor of Anderson following the first period after allowing two goals on 12 shots. Anderson stopped 22 of 25 shots.
"I thought it was a pretty easy decision," coach Pete DeBoer said. "I didn't like either of the first two goals. I didn't like the way the team was playing, either. I was hoping that it would be a shot of life there for our guys."
It was New Jersey's second victory over Florida in less than a week. The Devils beat the Panthers 3-1 victory at home on Nov. 20.
"We found a way, and that's important," New Jersey coach Brent Sutter said. "We did a lot of good things, but we have to use it as a learning experience. When we're in control like that, we can't let it slip away."
New Jersey led 2-0 before Bouwmeester got Florida on the board with 2:19 left in regulation on his first goal of the season.
Gionta opened the scoring 5:33 in with a power-play goal. He tipped Oduya's centering pass through Vokoun's legs.
Zajac made it 2-0 at 18:25 when he took a drop pass from Jamie Langenbrunner and fired a wrist shot that went through Vokoun's legs and bounced in off the right post.
New Jersey completely dominated the first half of the game and had a 25-7 shot advantage at one point in the second period. The shots ended up at 37-37.
"That's not an easy team to come back on," Weiss said. "But we found a way to do it and hopefully we can build some momentum from that."
Florida's first shot on goal in the second period came with 12:02 remaining. ... New Jersey C John Madden missed his third consecutive game because of a foot injury. ... New Jersey D Mike Mottau missed the game while serving the second of a two-game suspension for an elbowing incident against the Islanders.