Kovalchuk capped his evening by feeding Alexei Ponikarovsky, who scored the game-winner with two minutes and 39 seconds left in the first overtime.
"They were going to the bench [on a line change] and it was a great play by Kovy," Ponikarovsky said. "He saw me and made a great pass."
Besides scoring his first goal of the series, Elias helped break a 2-2 tie by feeding forward Zach Parise from behind the net. Parise stuffed the puck in the short side with 12:31 left in the third period.
In the third period, shortly after Kovalchuk hit the post, the Flyers tied the score, 3-3, when Danny Briere scored on a rebound with 8:56 left.
The Devils and Kovalchuk kept charging.
"I felt good today and was well rested with two days off. Sometimes you have to take one step back to take two steps forward," Kovalchuk said. "The guys played so well in Game 2 and you don't want to get back in the lineup just because you want to play."
Elias got things going for the Devils, scoring a power-play goal with 7:27 left in the first period that tied the score at 1-1.
He had gone the previous six postseason games without a goal. Elias is New Jersey's all-time postseason leader in goals (43), assists (79) and points (122), so it was only a matter of time until he enjoyed a breakout game.
"That was a great shot on the power play," Kovalchuk said. "It was really big and if he plays the way he played, we will be OK."
Just 20 seconds after Elias tied the score, Kovalchuk provided the Devils with a 2-1 lead.
Elias and Kovalchuk clearly gave the Devils a first-period spark. New Jersey dominated play in the first period, outshooting the Flyers, 14-7, in taking a one-goal advantage.
The spark lasted the entire game.
"We need him in the lineup," Parise said of Kovalchuk. "You can see what he does offensively, he makes things happen."
Kovalchuk said it was truly frustrating not playing in Game 2's 4-1 win.
"I felt better compared to almost the first series and first game of the second series," he said. "I thank the trainers and doctors who did a great job and hopefully I will move on and get better every day."
Contact staff writer Marc Narducci at 856-779-3225, firstname.lastname@example.org or @sjnard on Twitter.