Hossa's first goal came just 3:30 into the game, disproving the idea that the Red Wings might need time to get their legs back after five days of rest following a ten-day West Coast road trip.
Former Devil Brian Rafalski shot the puck in off the end boards behind goalie Kevin Weekes. Hossa jumped on the puck and put a quick shot to the near side off of Weekes and in.
New Jersey tied the game at 4:15 of the second period when Zach Parise tipped a shot by Johnny Oduya past Osgood.
Hossa scored his second of the night with 9:19 left in the middle frame, breaking into the New Jersey zone on a two-on-one with Tomas Holmstrom. Hossa faked a pass across and then snapped a shot between Weekes' pads to put the Wings back up by a goal.
Osgood was called on to preserve the lead with three minutes remaining in the period and the Devils on the power play. Patrik Elias drove to the net to deflect a Jamie Langenbrunner chance but Osgood dove across the crease, knocking the puck out of the air and grabbing it before it could cross the goal line.
Kirk Maltby added an insurance marker for Detroit, scoring his first of the season at 4:11 of the third period.
Notes: The Devils lost forward Brian Gionta with just over seven minutes remaining in the second period. Gionta moved to hit Detroit defenseman Derek Meech but Meech braced himself and put a shoulder into Gionta, who went down, hitting his head on the boards.