Aaron Voros scored twice in the third period for New York, and Ryan Callahan and Nigel Dawes added goals for the Rangers (6-1-1).
Scott Gomez and Brandon Dubinsky each had two assists and Henrik Lundqvist stopped 40 shots.
Hossa fired in a one-timed shot from the bottom of the right circle off a pass from Pavel Datsyuk. It was the 300th career NHL goal for Hossa, who eliminated the Rangers in the second round of last season's playoffs when he scored in overtime of Game 5 while with the Pittsburgh Penguins.
He left the Eastern Conference champions in July, signing a one-year, $7.45 contract with Detroit.
Hudler's goal, scored off a rebound during a power play following a questionable too many men on the ice penalty against the Rangers, tied the game at 4 with 3:39 left in the third period and forced overtime.
Voros' second goal broke a 3-3 tie 3:59 into the third when he banked in a shot off Osgood from the side of the net for his fifth of the season. He had tied it at 1:45 by tipping in Michal Rozsival's shot from the point.
Holmstrom's fifth goal gave the Red Wings a 3-1 lead with 9:03 left in the second. He deflected in a shot by Nicklas Lidstrom off the skate of Rangers defenseman Wade Redden.
Dawes closed the gap to 3-2 with 6:37 left in the second period with his first goal when he scored from the bottom of the right circle.
Detroit scored twice in the game's first 3:44.
Samuelsson opened the scoring just 28 seconds in when he tipped in Derek Meech's shot from the point. Franzen got his third goal, on a rebound, to make it 2-0, 3:16 later.
Callahan put New York on the board 7:32 in when he beat Osgood from the left circle.
