Jesse Puljujarvi also scored for the Oilers and Connor McDavid had two assists to help Jay Woodcroft get a win in his NHL coaching debut. Mike Smith stopped 37 shots, including 18 in the first period, to improve to 3-4-1 on the season.
Woodcroft moved up from Bakersfield of the AHL to replace the fired Dave Tippett on Wednesday.
"It's a good team win," Woodcroft said. "I enjoyed the way the game was played today. I thought our players really played hard for each other. Mike Smith turned in an 'A' performance and allowed us a chance to work our way into the game and I thought we got better as the game went on.
"It's been an emotional couple of days for this team, so I'm pleased for our players."
Edmonton snapped a two-game skid and improved to 6-2-1 in its last nine.
Hyman also praised Smith's play.
"He was phenomenal," Hyman said. "He gave us a chance the whole way through tonight, made some huge saves and was steady the whole time."
"We want to balance all the lines and have consistency in lines and I thought our game was good tonight, all four lines were going and we created a lot of stuff," Beauvillier said. "It's unfortunate we're getting out of here empty-handed."
Islanders coach Barry Trotz said his team probably should have had a first-period lead.
"I thought in the first period we had some really good looks," he said. "I thought we could have been up a couple of pucks in the first period. We didn't find the back of the net, that was a little bit of us and a little bit of Mike Smith."
Edmonton scored a rare first goal of the game when Ceci beat Sorokin with a long point blast with 57 seconds to play in the opening period. It was just the sixth time in the last 36 games that Edmonton got the game's first goal. The Oilers are now 13-0 this season when scoring the initial goal.
Edmonton made it 2-0 midway through the second period when Hyman elected to shoot on a 2-on-1 opportunity and got his 14th goal of the campaign and 100th of his career.
New York got back into the contest on the power play with five minutes to play in the middle frame as Beauvillier beat Smith glove-side.
The Oilers restored their two-goal lead on the power play midway through the third as Puljujarvi dove for a puck and swatted it through Sorokin's legs. His 11th ended a 14-game goal-scoring drought.