Celtic's reward for seeing off plucky Dunfermline last Sunday means they now take on lowly Kilmarnock at Rugby Park.
Dundee, who missed the chance to take on arch-rivals United, will host the winners of Raith Rovers' replay against Aberdeen.
And Europe-chasing Hibs entertain Ross County, who thrashed Stirling Albion in the last round.
Scottish Cup quarter-final draw: St Mirren/Rangers v Dundee United, Hibernian v Ross County, Kilmarnock v Celtic, Dundee v Raith Rovers/Aberdeen.
Ties to be played over the weekend of 13/14th March.
The games will be played over the weekend of March 13/14.