The hosts almost went ahead in the opening minutes but Gavin Swankie was unlucky to see his header rebound off the crossbar.
Dundee had most of the pressure early on and it was no surprise when they took a tenth-minute lead.
A defensive clearance fell nicely to the feet of Ross Harris and from 22 yards his right-foot shot flew past Peter Cherrie in the Clyde goal, giving the keeper no chance.
Dundee were then awarded a penalty on 42 minutes when new signing Derek Lyle was fouled by Robert Harris as he raced onto Callum McDonald's long ball.
Lyle stepped up himself and made no mistake from the spot, sending Cherrie the wrong way.
Swankie made it 3-0 on 48 minutes when he collected a pass from Alex Rae inside the box and after a good first touch, slotted the ball past Cherrie from ten yards.
Gary Arbuckle should have grabbed Clyde a lifeline a minute later but when all alone inside the six-yard area, he headed wide of the target.
Midway through the second half Swankie was unlucky again when his right-foot shot rebounded back off the upright.
Swankie should have made it four when he was one-on-one with Cherrie but his attempted lob was poor and the keeper saved easily.
Kevin McDonald fired just wide of the target and Swankie shot over the crossbar as the game moved into its closing stages.