San Jose has hit the skids and dropped its season-worst fifth in a row overall (0-4-1), including the first three of an eight-game Eastern road swing. The Sharks were 16-3-2 away from home on Jan. 1, but have gone 1-5-1 on the road since - losing four straight.
After Jonathan Cheechoo gave the Sharks a 1-0 lead with a power-play tally in the opening minute of the second, New Jersey stormed back on goals from Zach Parise, Madden and Brylin in a 10-minute span.
San Jose cut the deficit to 3-2 with 6:06 left on Kyle McLaren's goal that deflected in off the stick of Devils forward Brian Gionta.
Martin Brodeur earned his NHL-best 33rd victory.
Greiss made his third career appearance and second start in place of Nabokov, who sat for the second time in San Jose's 60 games. Greiss had a brief relief outing in the Sharks' 3-2 loss Monday to the New York Islanders after a shot broke the cage on Nabokov's mask and bloodied his nose.
Nabokov came back for the third period, but couldn't protect a 2-0 lead. With the Sharks playing their fourth game in five days Thursday in Philadelphia, Nabokov likely would've had a day off anyway.
San Jose center Patrick Marleau, the subject of trade rumors as Tuesday's NHL trade deadline approaches, rejoined the Sharks lineup after missing four games due to a groin injury. He had an assist, but it wasn't enough.
Shortly after Parise tied it 7:56 into the second, Madden tucked a shot in at the right post with 3:04 left to put New Jersey ahead. Brylin squeezed a shot under Greiss' arm, off a pass from Jay Pandolfo, at 18:06 to make it 3-1.
