Scott Gomez set up power-play goals by Patrik Elias and Brian Rafalski, and the clinching goal by Brian Gionta with 1:22 to play for New Jersey.
Devils goaltender Martin Brodeur, who set a single-season record with 48 wins, looked ordinary in making 23 saves in the game determined by power plays and turnovers.
Vincent Lecavalier scored twice to rally the Lightning from a 3-1 deficit. Martin St. Louis had the other goal.
Game 2 of the best-of-seven Eastern Conference matchup will be Saturday night at the Continental Airlines Arena.