Zach Parise and rookie Adam Henrique both posted 4 victory at the St. Pete Times Forum.
Ilya Kovalchuk, Petr Sykora and Dainius Zubrus also scored for New Jersey, which has won three of its last four games. Johan Hedberg earned his ninth win of the season with a 32-save performance.
Steven Stamkos scored two third-period goals for the Lightning, who are mired in a 1-7-0 slump.
Dwayne Roloson was pulled after allowing three New Jersey goals on 12 shots. Mathieu Garon made eight saves in relief.