The Detroit Red Wings were not about to lose two straight to last-place teams.
"It's important to get shutouts," Osgood said. "We want to start with trying to get one shutout period and move on from there."
"We were very upset with ourselves and we came out with a very solid and respectable win," said Brendan Shanahan, originally credited with Detroit's first goal.
The Islanders, last in the Atlantic Division with 42 points, have been playing their best hockey of the season. In the past week they earned a tie in Philadelphia and a victory in New Jersey two of the top three teams in the Eastern Conference.
"We know they work really hard and they just had a couple of big games," Shanahan said. "We didn't take these guys lightly at all. We had a lot of respect for them coming in and we played that way."
The shutout was Osgood's fourth this season and second in five starts. With his 27th shutout, Osgood, who has stopped 108 of the last 116 shots against, broke a second-place tie with Harry Lumley on the Red Wings' career list.
"We played well," Osgood said. "We didn't play really good in Chicago and we had to play a good game. They ere coming off a tie against Philly and beat New Jersey, two tough games, and we knew we were in for a good fight."
Islanders goalie Kevin Weekes continued his sharp play with 39 saves, but was the hard-luck loser. In five games, Weekes has allowed only nine goals on 178 shots and is 3-1-1.
"He's shown remarkable consistency in his game," Islanders coach Butch Goring said. "It's one thing to play with the lead, it's another thing when you're behind and have to keep us in the game. He's been doing both."
New York's Mariusz Czerkawski, playing in his 400th career game, saw his career-high 13-game point streak end in the loss.
"Of course I'm disappointed," Czerkawski said. "At the same time I'm disappointed at losing the game. I don't think we had the same motion or energy we had against New Jersey."
Detroit center Sergei Fedorov missed his second straight game because of a bruised knee. Fedorov, injured in Friday's loss to Los Angeles, is day-to-day.
Holmstrom gave the Red Wings a 1-0 lead late in the opening period. Steve Yzerman moved the puck into the right circle to Shanahan, who circled back and fired a shot that Holmstrom deflected past Weekes.
Holmstrom has 10 goals this season, three on the power play.
"We had to come out and try to play solid and I thought we did that," Osgood said.
Detroit outshot New York 12-5 in the first. Osgood stopped two point-blank attempts during a 3-on-2 in the last 15 seconds of the frame. Osgood also made two good saves with 5:50 left in the second to preserve the shutout.
"Czerkawski took a shot and hit my glove and the high guy banged it and it hit me in the chest," Osgood said of the first-period flurry. "He's been hot for them Czerkawski and that line they're the guys we were trying to key on to try and minimize the chances they were going to get."
The Red Wings improved in the second when they fired 17 shots at Weekes and held the Islanders to six.
Butsayev made it 2-0 at 6:30 of the second when he got just enough of the puck in a scramble in front of the net to trickle in his fourth goal.
The Red Wings also had a goal disallowed early in the period when Holmstrom backed into Weekes in the crease.
Islanders defenseman Eric Cairns returned from a four-game suspension received for a locker room hallway fight with Pittsburgh's Matthew Barnaby.
Detroit and New York will complete the home-and-home series, the teams' only meetings this season, Friday night at Joe Louis Arena.
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