The Devils, taking advantage of Jaromir Jagr's turnover, made it 3-1 when Kovalchuk scored from the high slot with 11 minutes, 52 seconds remaining. It gave him 30 goals, the ninth consecutive season he has reached that plateau.
A little more than six minutes later, Zach Parise scored a power-play goal on a rebound. Goalie Sergei Bobrovsky was slow to react.
Bobrovsky was the surprise starter in place of the sizzling Ilya Bryzgalov.
Defenseman Anton Volchenkov snapped a 1-1 tie early in the third period to give the Devils the lead for good. Volchenchov joined the rush and converted a pass from Kovalchuk, notching his second goal of the season with 17:15 remaining.
The Flyers had tied the score at 1 on a goal by Claude Giroux after just 16 seconds of the third period. Jagr went below the goal line and fed Giroux in front for his 25th goal, ending the Flyers' scoreless drought at 106:43.
With the win, the Devils tied the Flyers for points (85) in the battle for fifth in the Eastern Conference. The Flyers have a game in hand.
The teams will meet again Tuesday at the Wells Fargo Center.
It was Bobrovsky's first start since Feb. 12, a 4-3 loss in Detroit. The Flyers, looking drained from Saturday's 1-0 shootout win in Toronto, gave him little offensive support.
The second-year goalie got the call over Bryzgalov, who had started the last 11 games - and had shutouts in three of his last four performances.
Bryzgalov was spectacular Saturday in Toronto. He has not allowed a goal in the last 1:36.13, and he has stopped 135 of the last 137 shots he has faced.
"We had talked about this, looking at the schedule and what's coming up - the back-to-back," coach Peter Laviolette said before the game. "Eleven in a row, and every other night pretty much. It's a chance to get a fresh goaltender in there, and he'll be ready to play."
Bobrovsky was extremely sharp at the start, and made several impressive stops in the first period, including one in which he just got his glove on Alexei Ponikarovsky's shot from the side of the net late in the period.
The Devils, who had scored two late goals to notch a 2-1 win over the New York Islanders on Saturday night, capitalized on Braydon Coburn's slashing penalty.
Bobrovsky had no chance to stop Patrik Elias' power-play goal, scored on a tic-tac-toe passing play just 17 seconds after Coburn's infraction. Elias (24th goal) redirected a slick feed from David Clarkson to give New Jersey a 1-0 lead with just 25 seconds left in the opening period.
It was the first power-play goal the Flyers had surrendered in the last seven games, during which they had killed 14 in a row.
The Flyers, who entered the night with the league's highest goal-scoring average (3.22 per game), did not force Martin Brodeur to make many difficult saves in the first two periods, managing a total of 14 shots in those 40 minutes.
At that point, the Flyers were scoreless in their last five periods.
Contact staff writer Sam Carchidi at firstname.lastname@example.org or on Twitter @BroadStBull