Henrik Zetterberg had a goal and three assists and Detroit scored five power-play goals in a 6-3 victory.
"We got off to a real good start," Red Wings coach Mike Babcock said. "Obviously the power play was real good."
Detroit dominated the first period with three power-play goals as it outshot Calgary 22-4.
Lidstrom opened the scoring on a one-time slap shot from the right point at 4:31. Shanahan made it 2-0 when he tipped in Lidstrom's shot at eight minutes and Samuelsson tipped in Jiri Fischer's blast from the point with 3:32 left to complete the scoring for the period.
"We weren't as ready as we should be," said Flames captain Jarome Iginla. "If we take 'em, we've got to kill penalties. They had pretty much the whole first period in power plays and they earned that."
The Red Wings were 3-for-7 with the man-advantage in the period. Detroit finished the game 5-for-9 on the power-play.
Warrener got Calgary on the scoreboard 6:12 into the second period, when his shot from the point was accidentally tipped in by Detroit's Kris Draper.
Zetterberg added another power-play goal with 7:28 remaining in the second period when he scored from the inside edge of the left circle to make it 4-1.
Hamrlik then pulled the Flames to within two again with a slap shot from the top of the left circle with 5:06 left in the second.
Lang made it 5-2 with a one-timer from the slot with 36.9 seconds remaining in the second period.
Datsyuk added a power-play goal 8:05 into the third period.
Kobasew got his goal with 3:11 remaining.
Red Wings' goalie Manny Legace made 21 saves.
Flames' right wing Darren McCarty played his first game against Detroit since the team bought him out and he signed a two-year free-agent contract with Calgary. McCarty played 11 seasons with the Red Wings, helping them win three Stanley Cups.
"It went quick, it was like a wedding day," McCarty said of his return to Joe Louis Arena. "It just blew by."
He even leveled former linemate Kirk Maltby with a check 6:39 into the first period.
"I'm not mad at him or anything," Maltby said. "He's an aggressive player and he plays hard. That's what I would expect."
- Linesman Thor Nelson was hit in the face with a puck off the stick of Steve Reinprecht 3:29 into the game and was helped off the ice. He later returned.
- Lidstrom passed Ted Lindsay to move into sixth on all-time Red Wings' scoring list with 729 points.