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.
Copyright by STATS LLC and The Associated Press
Arena: Joe Louis Arena Location: Detroit, Michigan
Johan Franzen Assist: Nicklas Lidstrom, Brian Rafalski
Chris Chelios Assist: Mikael Samuelsson, Tomas Holmstrom
Henrik Zetterberg Assist: Mikael Samuelsson, Jiri Hudler
Pavel Datsyuk (power play) Assist: Henrik Zetterberg, Nicklas Lidstrom
Tomas Kopecky Assist: Dallas Drake, Kirk Maltby
Henrik Zetterberg Assist: Andreas Lilja, Tomas Holmstrom