WATCH: All Islanders vs. Coyotes highlights
"We need that win. We needed it a week ago, or two weeks ago," Vrbata said. "But to go on this break without a win … now everyone can feel a little better and take a few days to regroup."
Domingue won his first game since Nov. 8 against the Colorado Avalanche. He was itching to play after allowing four goals on 24 shots in a 4-2 loss against the Calgary Flames on Dec. 31.
"I'm not going to lie; I needed to prove something to everybody here in the room including myself," Domingue said. "It feels really good. I found a way and our group played super well in front of me."
Alan Quine scored in the second period and Thomas Greiss made 24 saves for the Islanders (15-15-8), who lost 2-1 in overtime at the Colorado Avalanche on Friday. The Islanders had 34 seconds of power-play time and six shots in overtime but failed to capitalize.
"That was probably the best overtime we have played all year and we still can't win a game," Islanders coach Jack Capuano said. "We had a stretch where (the offense) was going and now we are back to two goals in the last two games."
New York has points in six of the past seven games (4-1-2), but back-to-back losses on a two-game road trip after a five-day break was unsatisfying.
"We came in waves (offensively) in both games," Islanders forward Andrew Ladd said. "You have to find a way to win. It's tough to swallow when you need the points and you just can't find a way to come up with it."
The injury-riddled Coyotes were missing seven players, including forwards Martin Hanzal and Jordan Martinook, pressing defenseman Kevin Connauton into a forward role.
"If there had been a right winger walking by the arena, he would have been in the lineup today," Vrbata said.