Cummings steers Colorado past Columbus
It is the second consecutive season the Rapids have defeated Columbus in the play-offs after they won last year's Eastern Conference semi-final on penalties.
Cummings rifled a right foot shot past Columbus goalkeeper William Hesmer in first half stoppage-time after some superb build-up work by midfielder Brian Mullan and defender Kosuke Kimura.
The Crew's best chance to equalise came early in the second half when top scorer Andres Mendoza's shot slammed into the crossbar.
The Rapids will now host Sporting Kansas City, who topped the Eastern Conference, at home in the first leg of the semi-finals on Sunday.