Brodeur finished with 33 saves, including 13 in third period, as the Devils won for only the second time in seven games.
Dainius Zubrus scored twice in the third period and Damien Brunner also got a goal for New Jersey.
Jaromir Jagr registered two assists.
Anders Lindback was touched for three goals on 19 shots for the Lightning, who lost for the seventh straight time on the road.
2014: The Year in Music [PHOTOS]