Defenseman Sebastian Aho also scored for the Islanders, who have won two consecutive games and four of six. New York improved to 12-1-2 in its last 15 home games against the Oilers.
"What this game came down to is we were unable to solve their goaltender," Edmonton coach Jay Woodcroft said. "We didn't find a way to crack him."
The Islanders are 8-0-0 when the 38-year-old Parise gets a point.
Parise hasn't missed a game in his two seasons with the Islanders.
"It's fun playing with Zach. He made a great pass and I just put it in," Pageau said. "He's been helping me a lot."
"He's a big-moment guy, Islanders forward Cal Clutterbuck said of Pageau, who scored twice for the first time this season.
The assist extended Barzal's point streak to six games. Barzal leads the Islanders with 21 assists and 23 points overall.
"I thought we were committed to play the right way," Islanders coach Lane Lambert said. "And our goaltender played really well and made some great saves."
Sorokin made nine saves in the first, 17 in the second and 23 more in the third for his second shutout this season and the 12th of his career.
The Islanders denied three Edmonton power-play chances in the third as the 27-year-old Sorokin improved to 9-5-0.
"Three kills against them was huge," Clutterbuck added.
The Islanders were coming off a 2-1 overtime win Monday at Toronto. The Oilers lost their previous game, 5-2 at New Jersey on Monday.
The Islanders outshot the Oilers 12-9 in the first, though Edmonton didn't record a shot on goal until 13 minutes into the period. Sorokin's best save was a dazzling right pad stop on Zach Hyman at the 16:58 mark to keep the game scoreless.
Sorokin also denied Hyman from in close early in the third and Ryan Nugent-Hopkins with a snazzy glove stop with just under eight minutes remaining.
Campbell, who took a puck to the face on the bench during Monday's loss in New Jersey, made 28 saves in defeat.
"I thought he gave us a chance to win tonight and made some good saves when called upon," Woodcroft said. "I'm impressed with Jack Campbell and that level of stick-to-it-iveness and refusing to let a puck to the nose take a start away from him."
The Islanders are 13-2-0 this season when they score at least three goals.
The Islanders, who improved to 13-6-0, did not reach 13 wins last season until Jan. 18. ... Islanders forward Simon Holmstrom made his NHL debut after Kyle Palmieri was a late scratch with an upper-body injury. Holmstrom, a first-round draft pick in 2019, was recalled from Bridgeport and skated on a line with Barzal and Wahlstrom. ... New York also scratched defenseman Robin Salo and forward Ross Johnston. ... The Oilers scratched defenseman Ryan Murray and forwards Devin Shore and Kailer Yamamoto. ... The teams meet again Jan. 5 in Edmonton. ... Islanders defensemen have scored an NHL-leading 17 goals.
Oilers: Visit the Rangers on Saturday afternoon to complete a three-game trip to the New York area.
Islanders: At the Columbus Blue Jackets on Friday.
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