"I've played on this team long enough where I've had nights when I don't get very many shots," Osgood said. "I just stay focused on the puck."
Manny Legace stopped 35 shots for the Blues.
"We didn't play hard enough, and that starts with me," St. Louis coach Andy Murray said.
The Blues were whistled for 11 penalties, and two of the Red Wings' goals came on the power play. Their first and second man-advantage units each produced a goal.
"We have some pretty good players on the second power-play unit," Cleary said. "We have confidence in ourselves to shoot the puck at the net."
Zetterberg gave Detroit a 1-0 lead with a power-play goal just 22 seconds into the game. St. Louis' Eric Brewer took a delay of game penalty when he accidentally shot the puck over the glass in his own zone 16 seconds in.
"It just went downhill from there," Legace said.
Zetterberg scored his 15th goal just six seconds later after taking a cross-crease pass from Holmstrom.
Samuelsson made it 2-0 with another power-play goal 5:16 into the second period. He beat Legace with a wrist shot from the right faceoff dot for his third goal.
Cleary's breakaway goal with 5:47 left in the middle period gave the Red Wings a 3-0 lead. After a fake, Cleary beat Legace with a forehand shot that the Blues goalie got a piece of but it went in for Cleary's seventh of the season.
"We played 60 minutes," Detroit coach Mike Babcock said. "I thought we had a lot of jump and got good contributions from every player who dressed."
Lidstrom and Zetterberg lead Western Conference vote-getters in early fan balloting for the NHL All-Star Game. Lidstrom's 80,903 votes top the West, followed by Zetterberg with 58,074. Datsyuk is third among West forwards with 39,041 votes. ... Legace played with the Red Wings for six seasons from 1999-2000 until 2005-06, and Osgood played for the Blues in 2002-03 and 2003-04. ... Detroit center Tomas Kopecky injured a shoulder in the second period and didn't return. Babcock said Kopecky wouldn't play on Thursday against Nashville.