The Islanders dropped their fourth in a row after a 4-2-1 start.
"We deserved better tonight, there's no question," Islanders coach Jack Capuano said. "I felt the effort for 60 minutes was there."
John Tavares and Colin McDonald scored for New York, and Brian Strait had two assists. Evgeni Nabokov made 12 saves for the Islanders, who erased a pair of one-goal deficits but couldn't overcome a third even after Tavares was awarded a penalty shot with 3:53 remaining.
"We got to win hockey games, we have to get results," Tavares said. "We got to find a way to get points we need. We got to find ways to win and get back on the winning track and there's not much time."
The teams were tied 2-2 after two periods largely because of Miller, who made 27 saves through 40 minutes. He covered up for breakdowns by his teammates in the defensive zone and then turned aside Tavares' penalty shot with a glove save.
"We just need a win at this point," Miller said.
Miller, the 2010 Vezina Trophy winner as the NHL's top goalie, was also bailed out when Tavares hit the post on a semi-breakaway earlier in the third.
"I think with as many opportunities as we had, we got to put them in when we can," Tavares said.
Sulzer put the Sabres ahead for good 7:35 into the third, and Miller made sure they would leave snowy Long Island with a win. Sulzer's shot appeared to bounce off the ice and in the net over Nabokov's shoulder.
"Just one-timed it," Sulzer said. "Maybe (the puck hit him in a) tough spot."
Vanek, the NHL leader with 11 goals, opened the scoring 9:28 into the game. The forward was stationed in front of Nabokov and jammed a loose puck over him.
Tavares got the Islanders even at 1 in the final minute of the first period with his sixth goal of the season. After he got free from Ehrhoff, Tavares planted himself on the far side of the net before stuffing Brian Strait's shot past Miller.
Ehrhoff atoned for an earlier mistake by giving the Sabres a 2-1 lead 12:21 into the second with his first goal of the season. Ehrhoff, Vanek and Cody Hodgson played a three-man passing game through the neutral zone.
"(Hodgson) hit me back through the middle, and (I) put it in," Ehrhoff said. "That was definitely a good play."
However, that lead was also short-lived as McDonald scored the tying goal with 2:25 left in the second. He snapped a shot from the slot past Miller for his first goal of the season, and the second of his NHL career.
The Islanders got a pair of previously suspended players into their lineup for the first time this season.
Bailey was on the club's suspended list because of an injury he sustained while playing in Germany during the NHL lockout that prevented him from playing when the season started.
Visnovsky, acquired in a trade after last season, was suspended by New York after he chose not to report to the team when the lockout ended.
The defenseman attempted to have the trade overturned, and subsequently said through his agent that he wanted to play this season with HC Slovan of the Kontinental Hockey League.
The announced crowd of 12,608 alternated between booing Visnovsky and chanting "Lubo."
"I was pleased with his game for a guy who hasn't played for the last three, four weeks," Capuano said.
Bailey started the game on a line with Casey Cizikas and Matt Martin. Visnovsky was paired with Strait at even strength, and then with captain Mark Streit on New York's first power play. Bailey was even in 12:48 of ice time. Visnovsky logged 20:34.