The Stars held a 2-1 lead early in the second period, but Adam Henrique's shorthanded goal 3:35 into the middle stanza touched off the Devils' onslaught. Ilya Kovalchuk and Petr Sykora also scored in the second and Parise gave the Devils a 5-2 lead on a tip-in 9:19 into the third.
Parise has piled up eight points in his last three games -- and the four he had Friday were the most he has produced in one contest this season.
New Jersey won its third straight and prevented the Stars from capturing their fourth in a row. Dallas finished off a 3-2 road trip that took the Stars from California to New York.
Johan Hedberg made 33 saves for the Devils. Richard Bachman suffered his first NHL loss after winning his initial three starts. He stopped 31 shots.
Prior to the game the Devils retired jersey No. 27 worn by former defenseman Scott Niedermayer. He won three Stanley Cups with the team and is one of just three New Jersey players to have his number retired.