Kyle Calder had a goal and assist in his first game with Detroit, which is 10-2-2 in its last 14 games. Johan Franzen also had a goal and an assist for the Red Wings, who improved to 5-0-0 against Chicago this season and are 11-1-1 against the Blackhawks over the past two years.
Hasek lost a bid for his seventh shutout with a minute left in the third period when Jeff Hamilton scored on a wrist shot.
The Blackhawks are 1-4-2 in their last seven games. Their leading scorer, right winger Martin Havlat, sat out with the flu.
Calder was acquired by Detroit on Monday in a three-way trade with Chicago and Philadelphia. He had played 59 games with the Flyers this season.
Jason Williams, who was sent to Chicago in the deal, was in the Blackhawks' lineup.
Chicago's Nikolai Khabibulin blocked 24 shots.