The Red Wings reached the 100-point mark for the 12th straight season and, with 101, moved one in front of Nashville for fourth place in the Western Conference. Both have two games to play.
St. Louis, with the point it earned, is two back of Vancouver and the New York Rangers for the best record in the NHL.
Johan Franzen then scored twice for Detroit with the goals coming 2:15 apart. The second was scored with 3:50 to play in regulation.
Jimmy Howard made 27 saves for Detroit in its second straight win.
Brian Elliott gave up two goals on 28 shots. He came into the contest having recorded three consecutive shutouts.