Pavel Datsyuk also scored for Detroit and Dominik Hasek made 21 saves as the Red Wings won here for the first time since Nov. 20, 1993, a span of nine games that included two loses in the 1995 Stanley Cup.
Scott Gomez scored for the Devils, who dropped their third straight and fell to 11-3-1 at home.
Lebda got his second goal, the fifth of his career, with a sharp-angle shot from the left side that beat Martin Brodeur at 10:43.
Earlier in the third, Datsyuk pulled Detroit even with a power-play goal at 8:27. Mathieu Schneider hammered a point shot that sailed wide. The puck rebounded to Datsyuk, who drilled a shot into the New Jersey net.