Dominik Hasek made 18 saves for Detroit.
Scott Gomez scored for the Rangers.
Rangers goalie Henrik Lundqvist stopped 12 of 16 shots and was replaced by Al Montoya 10:37 into the second period.
Franzen gave Detroit a 1-0 lead just 28 seconds into the game when he put in a rebound of Lidstrom's shot for his fourth goal in four games.
Chelios made it 2-0 with 7:12 left in the period with his third goal in three games on a wrist shot from the right point.
Zetterberg put in Samuelsson's rebound 5:24 into the second period and Datsyuk added a power-play goal 2:07 later with Marcel Hossa in the penalty box for boarding.
Kopecky scored and Zetterberg added his second goal in the third period.
Gomez averted the shutout when he scored with 2:19 left.
Note: D Brian Rafalski made his debut with Detroit and got the second assist on Franzen's goal. He was signed from New Jersey as a free agent during the offseason. Rafalski, a native of suburban Detroit, missed the first five exhibition games with a hip flexor injury. ... New York defenseman Andrew Hutchinson grew up in suburban Detroit and played at Michigan State. ... Montoya played his college hockey at the University of Michigan.