St Mirren provided the best chance of the first half, when Joos Valgaeren was dispossessed in his own box by Buddies striker Martin Cameron, only for the striker to hit the side netting.
Celtic's first goal came from Henrik Larsson, just three minutes after the interval. A great ball slipped through by advid Fernandez found its way to Henrik Larsson, who slotted home for his 31st goal of the season.
Henrik's second came about 15 minutes later, when a great move by Celtic was finished off by the man himself, in delightful fashion.
The Bhoys' third came from Momo Sylla, who was set up by substitute Shaun Maloney for a tap in.
All in all a decent second half performance by the Hoops, though some players, such as Thompson, Fernandez and Sylla did not look interested.
Celtic now face either Airdrie United or St Johnstone in the next round at Parkhead, where we will be hoping for more of a crowd than the 29,000 that turned up today!
Celtic:
Hedman 7
Mjallby 6
Valgaeren 6
Laursen 7
Sylla 3
Healy 7
McNamara 7
Thompson 6
Smith 9
Larsson 8
Sutton 7
Subs used:
Fernandez (6)
Crainey (6)
Maloney (7)
Celtic-Mad Man of the Match: JAMIE SMITH