Fellow rookie Nick Palmieri tied it with 2:54 to play in regulation and Johan Hedberg made 20 saves and picked up an assist on the game-winner in helping the Devils win for the 10th time since Jan. 9 (10-1-2).
"The confidence is definitely higher than the first couple of months," Hedberg said after New Jersey moved within 15 points of a playoff spot following a poor start. "This is probably a game we would have lost earlier in the year. It was great to come back and get this one with the young guys getting the goals."
Rookie Jeff Skinner had two goals for Carolina, which moved a point ahead of idle Atlanta in the race for the eighth and final playoff berth in the Eastern Conference.
Brodeur hurt his right knee in a win Sunday over Montreal and the team listed his status as day to day.
Devils general manager Lou Lamoriello said the 38-year-old Brodeur will have to rehabilitate his knee before he can play again so it's unlikely that he will be back soon.
Tedenby's game-winner came on a counter attack. The Swede took a pass from Travis Zajac, skated between the circles and zipped a shot past Cam Ward for his seventh goal of the season.
He was benched for the third period in New Jersey's win Sunday over Montreal, the game in which Brodeur was hurt. He attended an optional skate Monday and then took his option not to skate Tuesday morning, something that surprised some of the veterans.
"It feels better for me than it did before," said Tedenby, also benched for six games in January because of his lackluster play. "I think I've learned a lot the last couple of weeks. It's been a good experience for me as a first-year player. I thought I did pretty good tonight, so I got the chance to play."
Palmieri forced overtime by backhanding the rebound of Ilya Kovalchuk's shot. The Russian skated through the Hurricanes' defense to take the shot and set up Palmieri's fifth goal in 15 games.
"At that point, all four guys were looking at Kovie, so I figured they weren't paying too much attention to me," Palmieri said. "I was just going to the net to look for the rebound."
New Jersey had three great chances to win in regulation, but Ward stopped a backhander by Jason Arnott with 2:12 left, made a glove on Andy Greene with 45 seconds to go and turned in a brilliant save in close on Patrik Elias with 14.4 seconds remaining.
Skinner, who also scored two goals in a 6-3 New Year's Day win over New Jersey, seemingly scored the winner at 8:37 of the third period with his second power-play goal of the game.
Just 6 seconds after Anton Volchenkov got his third minor penalty of the game -- the only three by New Jersey -- Skinner tallied his 20th of the season by tapping in the rebound of a shot by Eric Staal.
Skinner broke into the Devils' zone after taking a pass from Joe Corvo and beat Hedberg with a shot from low in the left circle that seemed to graze off the goalie's jersey and into the net at 9:22 of the second. It was Carolina's first shot of the period.
"I don't think the effort was there," New Jersey coach Jacques Lemaire said. "I didn't like the way we played. I didn't like our top players. I didn't like the guys who had the day off yesterday. I didn't like some of our defensemen. I didn't like a lot of stuff."
Skinner's 43 points and 23 assists are tops among NHL rookies, and his 20 goals rank second.
"When you have a lead like that, you're supposed to win the game," Skinner said. "We didn't play a sharp game tonight. The puck was bouncing everywhere. They have a lot of talent and they're playing a solid style of hockey right now."
Tedenby tied the game a little more than 2 minutes later after being set up right in front of Ward by a no-look pass from Arnott. The Hurricanes' goaltender never had a chance.
Troy Bodie, who hasn't scored in 43 games this season, had the best chance in the opening period when the rebound of Corvo's shot landed at his feet with the net open. However, the forward couldn't control the puck and the best he could do was slide a shot into Hedberg.
Material from wire services and team media was used in this report.
1 - 0 CAR
1 - 1 Tie
2 - 1 CAR
2 - 2 Tie
3 - 2 NJD