The teams waited more than an hour and 40 minutes before the Devils announced the game would be rescheduled.
The Lightning led 3-0 with 9:12 left in the period when the lights dimmed in the Devils end and could not be relit.
Steve Downie, Brandon Bochenski and Steven Stamkos scored for Tampa Bay.
The last time an NHL game was postponed was on Nov. 22, 2005, when Detroit defenseman Jiri Fischer had a seizure on the bench in the first period of a game against the Nashville Predators. Doctors had to perform CPR on Fischer.
The Lightning only had seven shots in the opening 30 minutes but three got behind Martin Brodeur, with the first two goals coming on the power play.
Downie deflected a point shot by Kurtis Foster past Brodeur at 6:58 of the opening period, and Tampa Bay got its other two goals in the second period before the lights dimmed and both were a little lucky.
Bochenski, who was recalled from Norfolk of the AHL on Jan. 2, scored on a quick shot from right in front after Rob Niederrmayer deflected a Stamkos pass right to him at 5:13 on another power play.
Stamkos scored a little less than 5 minutes later. Stamkos pushed a pass to Martin St. Louis and then took a return pass for a shot into a wide-open net.
Notes
Pierre-Luc Letourneau of the Devils and NHL penalty leader Zenon Konopka of the Lightning wrestled in the opening minutes and got 5 minutes each for fighting.