Sorokin preserved the shutout with 13 saves in the third.
"I like that we're trying to shoot the puck, but we've got to get them through," Eakins said. "When the opportunities are there, we've got to finish them."
The Islanders played without center Mathew Barzal (lower body) and defenseman Zdeno Chara (upper body), who are day to day after they were injured during a 5-2 loss at the Los Angeles Kings on Saturday.
"It's a next-man-up mentality," Cizikas said. "We wanted to go out there and we wanted to compete as a team."
The Ducks went 0-for-2 on the power play and are 0-for-9 over the past three games.
"They're known as a solid defensive team and they take care of their own end, so we knew it was going to be difficult," Anaheim defenseman Cam Fowler said. "We couldn't find a way to get one going. It's as simple as that."
NOTES: It was the first game between the Islanders and Ducks since Dec. 21, 2019, when Anaheim won 6-5 in a shootout. … Sorokin is the fourth active goalie with eight shutouts through his first 30 NHL wins, joining Martin Jones (10), Elvis Merzlikins (8) and Cam Talbot (8). ... New York blocked 20 shots, including seven by defenseman Ryan Pulock. … Dobson has scored nine goals since Dec. 5, the most by any NHL defenseman. He has eight points (three goals, five assists) in the past eight games. ... Islanders defenseman Sebastian Aho has an assist in five straight games. … It was the first multipoint effort for Johnston, who played his 100th NHL game. ... The Ducks are 1-2-0 on a six-game homestand. … Anaheim forward Max Comtois had one shot on goal in 14:29 of ice time after being a healthy scratch the previous two games. … Ducks center Adam Henrique did not play because of an illness. .... Lukas Dostal was recalled by Anaheim from San Diego of the American Hockey League and served as its backup goalie.