New Jersey was clinging to a 1-0 lead halfway through the middle period when Tampa Bay's Martin St. Louis coughed up the puck to Jagr at the Devils' blue line.
The 41-year-old veteran picked it up, skated in alone on Lightning goalie Ben Bishop and put a shot under the crossbar for the eventual game-winning tally.
It was the likely future Hall of Famer's 119th such goal, surpassing Tony Esposito for the most game-winners in NHL history.
Adam Henrique added a short-handed goal and Martin Brodeur made 16 saves as New Jersey won a second straight.
Steven Stamkos netted his ninth goal of the year for the Bolts.
Bishop finished with 20 saves.
2014: The Year in Music [PHOTOS]