Blake Comeau scored New York's lone goal with 9:25 remaining to spoil Clemmensen's bid for his first shutout since March 26, 2004. Clemmensen registered his second win in three starts on the trip to improve to 17-9-1.
"I almost had it," Clemmensen said of Comeau's rebound goal from the left circle. "I think this was as complete a game as we've played in the last two weeks. I think we're building off of our last two wins where we were a little bit up and down. But tonight we were fairly solid throughout most of the game."
Head coach Brent Sutter has seen his club take three in a row to move into a tie with Philadelphia for second place in the Atlantic Division, one point behind the first-place Rangers.
"I was pleased with the win," Sutter said. "Any time we come on the road like this, we need to move forward like we have been. We're 4-1 on this road trip. I think we played well. Our goaltending has been good, I've said that all along."
Special teams have been the difference for the Devils (27-15-3), who will host Montreal Wednesday in their final game before the All-Star break.
New Jersey is 2-for-2 on the man advantage over its last two games, and has converted six of its 12 power-play chances on the trip (50%). Devils' penalty killers have not allowed a goal (16-for-16) since the team hit the road one week ago.
"Our special teams have been really good the whole trip," said Parise, who leads the Devils with 26 goals. "The PK has been great. We're feeling good about ourselves right now. Everyone's playing well. It's good to get on the road for a while and be around the team and we're taking advantage of it right now."
The Devils dominated the scoring opportunities on the Islanders' first two power plays of the night.
Zajac made it 1-0 from the slot after Parise stripped New York netminder Yann Danis behind the Islanders' net. The third-year center tapped the loose puck into the vacated goal at 6:06.
With his 14th marker, Zajac matched his goal total from all of last season. He now has goals in three straight to go with seven points (4g-3a) in his last five games.
A hooking minor to Dainius Zubrus gave New York its second man advantage of the contest, and Zajac nearly made it 2-0.
Jamie Langenbrunner shoveled a backhand pass through Kyle Okposo to spring Zajac up the middle on a breakaway. He went glove side but was robbed by Danis at 8:16
The Devils had just a 1-0 lead to show for a first period in which they outshot the Islanders 13-7. They made up for it by striking twice in the first 4:58 of the second.
Parise pumped home his seventh power-play goal 57 seconds into the middle frame to put New Jersey ahead by two. Langenbrunner fired from the left circle toward Zajac in front, and Parise buried it from the right of the crease.
"I think it was a little shot-pass," Parise said. "I don't know if he was going for Travis there. I think it hit Danis' pad and went right to me. I had an open net. You always like getting those."
John Madden made it points in three straight by digging the puck out of the corner to set up Clarkson's blast through Danis at 4:58. Clarkson stretched his points streak to four games (2g-2a).
Comeau added his fourth from the bottom of the left circle, lifting Radek Martinek's rebound over Clemmensen at 10:35.
NJD NOTES Clemmensen has had a couple of near-misses with shutouts this season. Pittsburgh's Matt Cooke broke up a Clemmensen shutout bid with 3:58 left in the Devils' 4-1 win on Dec. 10. Florida's Jay Bouwmeester did the same on Nov. 26 with 2:19 remaining in regulation of a game the Panthers tied before the Devils triumphed in overtime... Patrik Elias assisted on Parise's goal to collect career point No. 679 and move within 22 of John MacLean's franchise record... Rolston's assist on Clarkson's tally gave him six points (3g-3a) in his last eight games... The Devils have five shorthanded goals this season.