The 684th goal of Jagr's 20-year NHL career put him one ahead of Hall of Famer Phil Esposito. Gordie Howe holds the record with 121, according to the Elias Sports Bureau.
Adam Henrique also scored and Martin Brodeur made 16 saves as the Devils won consecutive games for the first time this season and ended Tampa Bay's three-game winning streak.
Steven Stamkos, who had three goals and four assists last week, scored a power-play goal for Tampa Bay, which had won 5 of 6 in posting the best record in the Eastern Conference.
New Jersey, which lost its first seven games of the season, rallied late to beat Boston on Saturday for its second win.
Brodeur, who preserved Tuesday's win with a great reaction stop in front on Valtteri Filppula with five minutes to play, joked about Jagr being 41, just as he is.
"He's been around a long time, longer than me actually, and that's pretty tough to say," Brodeur said. "This guy is amazing, the way he plays the game. I knew of him and played against him when I was younger so I can't say anything about his past, but what I have seen in his three months here, it's pretty amazing to see him go. Not just the way he plays, but in the room and the way he conducts himself."
Jagr's third goal of the season came midway through the second period when he stripped Martin St. Louis at the Devils' blue line and broke in alone for a 2-0 lead. Both New Jersey goals came on turnovers at the blue line.
"On both goals we shot ourselves in the foot," Lightning coach Jon Cooper said. "We gave a first-ballot Hall of Famer a clear-cut breakaway from their blue line. There's a really good bet that might go in the net."
The Devils dominated the opening 35 minutes, jumping to a 1-0 lead at 1:36 of the second period when Henrique tallied short-handed against Bishop, who made 20 saves in losing for the second time this season.
Henrique knocked down a pass that defenseman Matt Carle tried to send from left point to the corner and it set up an odd-man rush. Henrique carried the puck into the Tampa Bay zone and then played a give-and-go with Patrik Elias on cross-ice passes, beating Bishop before he could get back into position.
Tampa Bay, which had four shots in both the first and third periods, finally woke up after a penalty in front of the net by Henrique at 14:15 of the second put it on a power play. Stamkos swatted in his own rebound while falling to the ice to cut the deficit to 2-1 at 15:23. It was his ninth goal of the season.
"We sustained pressure and got back into the game and we could have had the lead," Cooper said. "Why can't we do that for more than six minutes a game. That's the frustrating part."
While Brodeur didn't face many shots in the opening two periods, he had to make several big saves. He made a point-blank save on Alex Killorn seconds before Henrique was called for his penalty and stopped Carle in close after Stamkos scored.
Brodeur also stopped Tyler Johnson on a first-period breakaway and got a little help when a B.J. Crombeen shot caromed off the iron.
Elias appeared in his 1,100 NHL game. ... Lightning D Eric Brewer played in his 900th. ... Brodeur made his second straight start with Cory Schneider out with a lower back injury. ... Tampa Bay has scored power-play goals in four straight games. ... Henrique's short-handed goal was the Devils' second of the season. ... The loss also snapped the Lightning's three-game road winning streak, its longest since 2007-08.
Information from The Associated Press was used in this report.
Copyright by STATS LLC and The Associated Press
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