Carter finished with two goals as the Flyers took a stranglehold of their exhilarating seven-game tug-of-war with their rivals from up the Jersey Turnpike.
The Flyers lead the first-round series, three games to one, with Game 5 in Newark on Thursday.
In the franchise's history, the Flyers have a 17-2 series record when they have a three-games-to-one lead. The only times they have lost a three-games-to-one series lead: 1988 against Washington, and in 2000 against New Jersey.
Goalie Brian Boucher again outplayed Martin Brodeur - who was denied his 100th career playoff win - as the Flyers won for the eighth time in 10 meetings with the Devils this season.
The fans showered Brodeur with mocking chants of "Mar-tee, Mar-tee" throughout the second and third periods.
Third-period goals by Dan Carcillo and Carter (on a five-on-three power play) enabled the Flyers to pull away from a 2-1 lead. Simon Gagne suffered a lower-body injury and did not play in the final period. Gagne appeared to get hurt blocking a second-period shot.
With 15 minutes, 31 seconds left in the second period and the Devils holding a 1-0 lead, Brodeur showed why he is hockey royalty.
Prone on his side, the all-time leading winner in NHL history somehow gloved Gagne's bullet from the slot. Gagne had taken a slick back pass from Mike Richards and appeared to have Brodeur measured.
But the almost-38-year-old goalie showed the reflexes that have made him a legend.
Undeterred, the Flyers kept applying pressure and it resulted in the tying goal, a power-play score by Carter with 10:52 left in the second.
Carter scored from the left circle, notching his first goal of the playoffs and offsetting an earlier goal by Ilya Kovalchuk, who had also been struggling in the series. It was Carter's first goal in the six games he has played since returning from a broken left foot.