The result was a 4-1 win Tuesday night that ended their two-game losing streak.
"We just didn't throw the puck away," Islanders defenseman Brad Lukowich said. "We showed more composure. We were on the road, so we simplified things."
Rick DiPietro made 25 saves to hold the Devils at bay.
"It was kind of gloom and doom around here after those two loses," DiPietro said. "The guys came out with a sense of urgency. We weren't laying back."
Vladimir Malakhov scored for the Devils, who dropped their fourth straight.
"We need to get more contributions from everybody," Devils coach Larry Robinson said. "This was a night I thought the Islanders were as fragile as we were. We had the chance but we gave up a couple of bad goals."
The Islanders took a 2-0 first-period lead on goals by Weinhandl and Bates.
Weinhandl deflected Lukowich's point shot past Scott Clemmensen at 2:57.
Bates scored from a difficult angle at 11:35. Bates took a shot from the right boards as he drove toward the goal line and the puck slipped past Clemmensen.
"It was a bad bounce on the first one, a bad goal by me on the second," Clemmensen said. "From there, it was uphill the whole way."
In the second, Malakhov scored on a 5-on-3 advantage at 7:11 to cut it to 2-1. Malakhov, manning the right point, took a cross-ice feed from Paul Martin and fired a shot past DiPietro with Brian Gionta providing an effective screen.
The Islanders countered with Kvasha's power-play goal with 2:21 remaining in the period. Brent Sopel took a point shot that glanced off Kvasha's leg,
New York threatened to add another goal in the closing seconds but Blake hit the left post on a short-handed breakaway.
In the third, the Devils mustered only seven shots and DiPietro turned them all away including two from close range by Jay Pandolfo.
Blake closed out the scoring on 2-on-1 break with Bates with 1:02 remaining.
- D Dan McGillis and RW Alexander Mogilny were healthy scratches for New Jersey. The Devils have been frustrated by Mogilny, the former 76-goal scorer. He sat out his first game after scoring one goal in the last seven games. Darren Langdon took Mogilny's place and saw his first action of the season.
- Devils G Martin Brodeur missed his sixth straight game because of a sprained medial collateral ligament in the right knee.
- New York ended a three-game road losing streak.