The save came 64 seconds after Nielsen cut the lead to 2-1 by beating Miller on the short side with a slapper from the left circle.
Sabres coach Lindy Ruff wasn't complaining, crediting Miller for making several clutch saves, particularly a pair 6½ minutes into the second period. That is when Miller stopped Brian Rolston on a breakaway and then recovered in time to get his chest out to foil Josh Bailey on the rebound.
"You're going to need big saves inside of every game," Ruff said. "That was back-to-back great saves. The great saves like that usually lead to victories for you."
The inconsistent Islanders are 4-5-1 in their past 10 games. They at least scored, as Nielsen's goal snapped New York's drought at 106 minutes, 51 seconds, a day after a 6-0 home loss to Ottawa.
This is no time to panic, said assistant coach Doug Weight, who filled in behind the bench because head coach Jack Capuano was sick with the flu at the team hotel.
"If you sit on the plane, you look at it as catastrophic," Weight said. "But as tough as it is, when teams are struggling, it can change in a hurry. So we have to get our swagger somehow offensively back. And it's there to be had."
Moulson, who leads the Islanders with 25 goals, was well aware of the opportunity he had in the third period.
"We've got to learn from the mistakes we made and some of the chances we gave up, and move on," said Moulson, who said the puck bounced and prevented him from lifting a shot over Miller. "There's no time to feel sorry for ourselves."
Islanders goalie Kevin Poulin rebounded and stopped 35 shots, a day after he was yanked after allowing two goals on five shots against Ottawa in 1:35 of action.
Myers opened the scoring 1:21 in during a scramble in front. After Poulin stopped Roy and then Pominville, he had no chance when Myers streaked in from the point and flipped the loose puck over him.
Poulin also had no chance on Vanek's goal, scored 3:41 into the second period after a bad line change by the Islanders.
Rather than going immediately to the bench, Rolston chased down the stick he dropped in the Sabres' corner. He didn't realize teammate Matt Martin was still behind him, limping off.
Enjoying what essentially became a 5-on-3 advantage in the New York end, Roy parked himself behind the net and fed a pass into the slot, where Vanek snapped a shot in the open side.
Roy has suddenly rediscovered his offense. After managing four goals and two assists in 23 games, he has two goals and five assists in his past four.
"We're happy, but at the same time, we've got to get some more points," Roy said. "We've got to keep winning hockey games. We can't win one, lose one anymore. We've got to put a streak together. We've got to gain some ground right now."
Ruff listed Sabres D Robyn Regehr as day-to-day after he left with an undisclosed upper body injury in the first period. ... Bailey didn't return for the third period because of back spasms. ... Capuano traveled with the team to Buffalo on Monday but was unable to attend the team's morning skate Tuesday. ... The Sabres went 0-for-1 on the power play and have converted just one of 33 chances in 12 games.
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BUFFALO, NY - FEBRUARY 21: Derek Roy #9 of the Buffalo Sabres heads to the ice to warm up for a game against the...