Jimmy Howard stopped 41 shots and improved to 10-3-3 in 16 career appearances against the Rangers.
Andreas Athanasiou scored twice and Jonathan Bernier stopped 41 shots for the Red Wings
Detroit held 3-0 lead in second period.
The Red Wings have dropped their last nine games against the Habs.
Barkov scores 30th goal as Florida Panthers pound Detroit Red Wings 6-1.
Tampa Bay became the first team this season to clinch a playoff berth.
MacKinnon’s goal in extra session sends Detroit to eighth straight defeat, 4-3.