Coventry went ahead early on with Clarke volleying home in the sixth minute after a cross from Blair Adams.
And the Sky Blues added a second in the 32nd minute when Carl Baker pulled the ball back from the byline on the right and Callum Wilson fired into the roof of the net from 12 yards out.
Coventry made it 3-0 in the 49th minute when Clarke netted his second after collecting the ball on the edge of the area and firing a low shot into the corner.
Sheffield United pulled one back in the 62nd minute when Lyle Taylor scored with a low 25-yard free-kick.
And a minute later City stopper Joe Murphy saved Ryan Flynn's shot from close range as United went close to adding a second.
Clarke almost scored his third goal in the 70th minute but his low strike was saved by George Long in the United goal.
The Blades made it 3-2 in the 80th minute when the unmarked Taylor headed in his second goal after a cross from the right from Ryan Hall.
But Coventry held on for the win to go 16th in League One, while Sheffield United remain bottom of the table.