Vrbata's shootout goal was the 44th of his career, the most in NHL history.
The Coyotes have taken 12 shootout shots this season and scored on seven of them. That's a 58.3 percent success rate, which is tops in the NHL.
"We're not trying to get it to there, but if it gets to there we feel like we have people that can score," Head Coach Dave Tippett said.
• The Coyotes played minus forwards Martin Hanzal and Jordan Martinook. Hanzal suffered a lower-body injury in Friday's game at Anaheim. Martinook suffered an upper-body injury in the same game. Both players are considered day-to-day.
Because they were shorthanded at forward, defenseman Kevin Connauton played right wing on the fourth line.
Connauton, who played forward once before in the NHL while with Columbus, played 7:06, took one shot on goal and delivered three hits.
"I give Kevin Connauton a ton of credit," Tippett said. "He's a left defenseman that played right wing today. He did a heck of a job."
• Goalie Louis Domingue made six of his 27 saves in the five-minute overtime. It was a nice comeback game for Domingue, who allowed four goals in his previous start vs. Calgary on New Year's Eve.
Domingue's lone blunder came in the second period when he launched an errant pass up the middle of the ice that was intercepted by Islanders defenseman Johnny Boychuk and quickly parlayed into a goal by Alan Quine.
"The play should have been on the wall, but I don't know, I saw an opening there," Domingue said. "... We found a way to bounce back ... Our group played super well in front of me. They blocked a lot of shots and our penalty kill was great tonight."