Artemi Panarin, the Rangers' leading scorer with 68 points (26 goals, 42 assists), missed his first game this season because of an upper-body injury he's been dealing with for five days that hasn't improved, coach David Quinn said.
"We were kind of 50-50 throughout the afternoon whether he was going to play and by the end of it, it didn't seem like the right thing to do," Quinn said. "We don't think it's long-term."
Panarin, who was to represent the Rangers at 2020 Honda NHL All-Star Weekend at Enterprise Center in St. Louis, will not attend and will be replaced by forward Chris Kreider.
Pavel Buchnevich and Kreider scored power-play goals in the third period for the Rangers (23-21-4), who have lost two in a row. Mika Zibanejad had two assists and Alexandar Georgiev made 14 saves.
The Rangers don't play again until Jan. 31.
"It would have been a lot nicer to leave after a win tonight, but I think these nine days will do us good," Zibanejad said. "We obviously have a whole lot of hockey left to play and the way we're trending, we get this break here, come back, regroup and just go at it when we come back."
Bailey gave the Islanders a 1-0 lead with a power-play goal on a deflection of Noah Dobson's shot from the blue line at 13:35 of the first period.
They connected again on the power play three minutes later when Anthony Beauvillier scored on the rush with a wrist shot to make it 2-0 at 16:35.
The Rangers tried to generate a shorthanded scoring chance, but Greiss made a save on Jacob Trouba, who got stuck in the zone with Ryan Strome, allowing the Islanders a clean 3-on-2 breakout that led to Mathew Barzal (two assists) setting up Beauvillier.
"We made a bad decision," Quinn said.
Anders Lee scored with a one-timer from above the left circle at 9:52 of the second period to give the Islanders a 3-0 lead. Jordan Eberle won a battle for the puck behind the net and Barzal won another in the corner before passing to Lee.
"I got a good bounce on it, but it's those two battles that they won to get me the puck and we got rewarded for it," Lee said.