Making his 19th consecutive start, Vokoun needed 241 games to move past former Devil Mike Dunham, who had 81 wins in 217 games with Nashville. The 27-year-old Czech surrendered a goal to John Madden in the final minute but withstood a late flurry.
Legwand opened the scoring on the power play in the first period and was credited with the eventual game-winner 5:20 into the third.
Defenseman Mark Eaton had the other goal for the Predators, who had been 0-4-0 all-time at home against New Jersey. But Nashville is unbeaten in 10 of its last 11 home games (7-1-2-1).
Patrik Elias also scored for the Devils, who are winless in five of their last six games (1-2-2-1).