Jiri Hudler, and Pavel Datsyuk scored for Detroit (29-12-5), which won its fourth straight.
Hasek, who leads the NHL with a 1.98 goals-against average, is one shutout behind New Jersey's Martin Brodeur for tops in the league. But it wasn't enough to earn a spot on the Western Conference all-star team.
David Aebischer made 37 saves for Montreal.
Detroit defenceman Chris Chelios played in his 1,515th career game and moved past former Red Wings captain Steve Yzerman into 10th place on the career list. Yzerman retired after last season, his 22nd - all with Detroit.
The Red Wings took a 1-0 lead 9:18 in on Hudler's seventh goal. He beat Aebischer with a slapshot from the top of the left circle, high on the far side.
Datsyuk added his 13th goal, when his shot from deep along the right boards got between Aebischer's arm and body.
Notes: Hasek is ninth on the career shutout list . . . Montreal and Detroit last played on Oct. 20, 2003 . . . Montreal D Mathieu Dandenault played in Detroit for the first time since signing with Montreal in Oct. 2005. He played nine seasons with the Red Wings (1995-2004), helping the team win three Stanley Cups . . . Detroit D Mathieu Schneider missed his fourth game with a strained knee ligament.