"We played a great game both ways tonight," Deslauriers said. "We worked hard for our chances and we played smart. Defensively, we were really on the button tonight. Everyone was committed to doing the job."
Edmonton also beat Minnesota on Friday night to snap a three-game losing streak. Last overall in the NHL, the Oilers are 6-25-2 in their last 33 games.
"He's been really sharp in both games," Oilers coach Pat Quinn said about Deslauriers. "We were pretty good in front of him, too, but he made some big stops when he had to. He looked sharp.
"He wasn't sitting back like he does when he doubts himself every once in a while. He's not guessing right now. He is playing like he knows what is happening out there."
Martin Brodeur stopped 33 shots for the Devils.
"He is somebody I have admired since I was a kid, I think he's the strongest goalie mentally in the league," Deslauriers said. "You play against somebody like that, who you watched growing up, and see him during the warmup across the ice. You're thinking, is this real?"
New Jersey, coming off a 5-3 loss in Calgary on Friday night after opening its three-game trip with a victory in San Jose, is 2-10-1 in its last 13 road games.
"I don't know what the reason was, but especially in the first 40 minutes we were just bad," Devils center Dainius Zubrus said. "They were outskating us. We weren't good on the forecheck. Wee weren't creating anything, just throwing the pucks away.
"They were better than us. We had a few chances in the third, their goalie made a few saves, but that was nowhere good enough to win a hockey game."
Edmonton opened the scoring 1:23 into the second. Patrick O'Sullivan tracked down a puck behind the New Jersey net and put in front to Brule. His quick shot banked in off of Brodeur for his 14th goal and 30th point of the season.
"Our focus wasn't there. Our legs weren't there," New Jersey coach Jacques Lemaire said. "Maybe we felt that because we were playing a team that doesn't win a lot of games, we could just go through the motions. But we've talked about this all year. To win games you have to work."
The Oilers stretched their lead not long after when Robert Nilsson dove to make a pass to Pouliot, who blew a shot past Brodeur for his fourth of the season.