Couture opened the shootout by slipping a backhander between the pads of Dwayne Roloson. P.A. Parenteau then shot high before Joe Pavelski was stopped.
Antero Niittymaki made a beautiful glove snare of a Frans Nielsen high backhander before Dan Boyle sealed the win as he lifted a backhander past Roloson.
Boyle scored in regulation while Niittymaki stopped 24 shots for the Sharks, who had dropped three of four coming in.
“We’re at home, we’ve got to make it count,” Boyle said. “It’s a pretty long homestand, I think five games total. It’s important right now to get some of those points we lost earlier in the season.”
Parenteau netted a goal and Roloson stopped 37 shots in the loss for the Islanders, who have dropped nine straight for the first time since losing 10 in a row from December 4-23, 2008.
After a scoreless first period, Parenteau gave the Islanders the initial lead as he skated around from the left boards to the slot and zipped a wrister over the glove of Niittymaki at the 4:51 mark.
Skating with a 5-on-3 advantage, the Sharks tied the game when Pavelski fired a pass from the left circle to the top of the right circle where Boyle snapped a wrister through traffic with 5:34 left in the frame.
Niittymaki stopped 10 shots through the third period and overtime while Roloson made eight saves the rest of the way.
The Sharks continue their five-game homestand on Saturday against Calgary…The Islanders wrap up their three-game road trip in Los Angeles on Saturday…San Jose center Joe Thornton returned to play after serving his two-game suspension for an illegal hit versus the Blues on November 4…The Sharks have taken three straight and five of the last six against the Islanders.