Chris Sutton grabbed his sixth goal of his Celtic career as the holders crushed their First Division opponents to progress into the fourth round.
The £6 million striker lifted a poor cup tie and fired home to open the floodgates at Parkhead. Striker Tommy Johnson added a second and Raith's misery was compounded just after the break when Alex Burns was red-carded before Johnson grabbed his second of the night and £2.75 million Alan Thompson scored the fourth.