Osgood made 29 saves for his 50th shutout and 394th career victory.
"I don't put much merit in shutouts," he said. "The only thing they're good for is that you know you have a great chance of winning the game. I grew up watching Grant Fuhr play and he was just about winning games, so that's kind of my mentality."
Osgood, though, acknowledged he's trying not to think about win No. 400 because it "is big for me."
Henrik Zetterberg and Tomas Holmstrom scored in the first period to generate more than enough offense against a team that is struggling to score and didn't get any puck luck, hitting the post in both the first and second periods.
The Bruins have not scored in nearly 133 minutes, getting shut out in consecutive games for the first time since March of 2007.
"We're going to have to decide that we're tired of hearing we had a good effort without winning," Boston coach Claude Julien said.
The Bruins pulled Tim Thomas with about 1 1/2 minutes left to add an extra skater and called a timeout in the final minute, trying to come up with a way to pull within a goal.
It didn't happen.
Thomas had 24 saves for Boston, which fell under .500 with their third loss in four games.
"I made a couple of mistakes that ended up costing us," Thomas said. "We couldn't put the puck in the net."
The rebuilding Red Wings are 3-0-1 in their last four games and have a point in seven of their last eight.
Lucic is out with a broken finger and Savard has a broken foot.
The Red Wings have relied on Holmstrom all season, and lately they've been able to lean on Zetterberg and Pavel Datsyuk.
Holmstrom has 10 points this season. Zetterberg has bounced back from a slow start with nine points in his last nine games. Datsyuk has had at least two points in four of his last five games.
Zetterberg's third goal of the season came 2 seconds into a power play after Datsyuk pushed the puck toward the net from the left circle off a faceoff.
Holmstrom's eighth goal in 13 games came trailing on a rush after Datsyuk made a nifty drop pass off an up-ice feed from Todd Bertuzzi.
"He's got eyes in his back," Holmstrom said.
Michael Ryder and Marco Sturm both had a good chance to score, but got unfortunate caroms off a post behind Osgood. ... Detroit's Jonathan Ericsson (flu), Brian Rafalski (flu) and Brad May (eye) were scratched from the lineup. ... The Bruins were the only team Holmstrom had not scored against in his career. ... The Original Six teams are not scheduled to play again this season.