New Jersey was one for 10 with the extra man in dropping a pair of one-goal decisions at Carolina to open the best-of-seven series. But the two-time defending Eastern Conference champions went three for seven on the power play and ended a four-game post-season losing streak.
"Special teams is always a big part of playoff hockey and tonight we made some adjustments and were able to score goals on the power play," Devils captain Scott Stevens said.
"Coming into today, we just wanted to win one game and get back into it. We did a lot of little things right, played a physical game, didn't give them a lot of room and we got into their faces."
The Devils dominated the first period, chased goaltender Arturs Irbe in the opening minute of the second and outshot Carolina, 35-16. Brodeur recorded his 13th career playoff shutout and third against the Hurricanes.
Game 4 will be played Tuesday night in New Jersey.
"I think we were able to get Irbe off his game," said rookie Brian Gionta, whose inability to clear the puck in Game 2 led to Bates Battaglia's overtime winner. "We were able to get in front of him and create some problems. I think one of the differences for us tonight was that we did not have as many of our shots blocked."
Brodeur was hardly tested but stopped rookie Jaroslav Svoboda's wrist shot from the right faceoff circle on a two on one with just over two minutes to go in the first period.
By then, New Jersey was in control with a 2-0 lead.
Gionta got things going at 7:48 with his first career playoff goal. Irbe stopped Bobby Holik's blast from the top of the left circle but could not control the rebound. Gionta beat defenseman Niclas Wallin to the loose puck and put it into a half-empty net.
"Bobby put the puck on net and I just had to put home the rebound," Gionta said. "It was lying there for me. We need to put pucks on net and in playoff hockey, anything can happen. That play proved it."
Just over a minute later, Carolina captain Ron Francis was penalized for hooking, giving the Devils their second power play. They needed just 33 seconds to score as Rafalski wristed a shot from above the slot through traffic and past Irbe.
"Had we scored a power-play goal in Game 2, we probably would have won," Rafalski said.
The Hurricanes went 12 1/2 minutes without a shot in the first period and New Jersey had four power plays before Carolina got its fourth shot.
"We didn't get any breaks around the net tonight and we were not quick at all," Hurricanes coach Paul Maurice said. "We were slow in everything we did, and part of that was that they were very quick and made us look slower."
Carolina rookie Erik Cole, who had a goal in each of the first two games, took a roughing penalty with 57 seconds to go in the opening period, giving the Devils an advantage that carried into the second.
At the 58-second mark, Holik used Gionta as a screen before scoring on a slap shot from the top of the left circle that ended Irbe's afternoon.
"It was not my decision," said Irbe, who stopped nine shots. "I'm not surprised by anything, it's the playoffs. The difference tonight was I let in three goals. The first one hit me in the blocker and I dropped it. I didn't see the other ones. Still, I have got to stop them."
"He understands what time of year it is and he will bounce back with a great effort," Francis said.
Kevin Weekes made his NHL post-season debut but was beaten on the sixth shot he saw as Rafalski fished out a loose puck in the slot and chipped it in to complete his second career two-goal playoff game.
Gionta nearly got his second of the game with 2:56 to go in the period, but the video replay official ruled his stick was above the crossbar when he tapped his own rebound past Weekes.
Moments later, Carolina had one more chance to avoid the shutout, but Brodeur squeezed his pads to deny Francis on a partial breakaway.
Holik also had a shot at a two-goal game, but he put a slapper off the left goalpost with just over eight minutes to go in the third.