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.
The Devils pressured for the equalizer in the closing seconds with a three-man advantage with Brodeur pulled for an extra attacker and two Red Wings serving penalties. Hasek managed to keep the puck out despite intense Devils pressure in front of his net.
Gomez broke a scoreless game in the second period on a power play set up when Hasek was called for two penalties at 9:27. The goalie was initially whistled for playing the puck in the area behind his goal. Enraged by the call, Hasek smashed his stick - drawing an unsportsmanlike-conduct penalty.
Gomez cashed as he deflected Brian Gionta's blue-line shot past Hasek at 10:57. For Gomez, the goal was his fourth of the season and first on the power play.
The Red Wings peppered Brodeur with shots in the scoreless first period. Detroit outshot New Jersey 13-6 and got one of its best chances late in the period when Brodeur stopped Henrik Zetterberg from close range.
The Devils went six minutes without a shot but their first was a breakaway by Travis Zajac that Hasek blocked.
Notes: Brodeur was back in goal for New Jersey after a rare night off. Backup Scott Clemmensen was the loser in the Devils 5-3 loss to the Boston Bruins on Thursday. Brodeur has started 29 of the Devils 31 games. . . . Brodeur entered the game with a record of 11-6-0 and a 1.99 goals-against average in 18 games-including playoff-against the Red Wings. . . . Defenceman Niklas Kronwall returned for the Red Wings after missing six straight games with a groin injury.