Broadwood Stadium stood tall in the face of Storm Ciara but brave Clyde fell as a changed Celtic side blew them away.
Goals from Olivier Ntcham, Scott Brown and substitute Vakoun Bayo was enough to make sure that the Parkhead side were in the hat for the quarter final draw.
The Bully Wee were packed into their own box by the Scottish Cup holders and just could not break down the hoops defence when they went forward either.
Early on however the Cumbernauld side looked lively and managed to create a couple of chances before the deadlock was broken.
Mark Lamont had a shot deflected for a corner early on as his strike was blocked by french defender Christopher Jullien.
John Rankin wanted in on the action but he sent his effort high over Scott Bain’s goal.
It was on the 16th minute though when the Premiership leaders took the lead with a curling effort from Ntcham.
The midfielder received the ball from Boli Bolingoli on the left hand side and as he made his way inside he unleashed a right foot shot which bounced in front of Clyde keeper David Mitchell and into the bottom corner.
Celtic rained on Clyde’s parade as captain Scott Brown added his name to the score sheet for the Premiership side’s second goal.
Brown directed a Patryk Klimala flick into the net with the outside of his boot in the six-yard box as he beat Barry Cuddihy to the loose ball.
Bully Wee captain David Goodwillie was on the end of a long ball before the end of the first half and his run along the byline into the Celtic box came to nothing as there were no white shirts for 40 yards to help him out.
Celtic dominated for large periods of the match but Raymond Grant eventually won the ball in the middle of the park and ran into the Celtic box but he couldn’t quite make the pass to the waiting Goodwillie.
Despite not showing any signs of giving up the visitors wrapped up the game when forward Bayo tucked the ball away.
Austrian international Moritz Bauer bombed forward in the 90th minute and beat two men on his way to the byline and his cross found Bayo alone inside the clyde penalty area who side-footed the ball into the empty net.