Coventry doubled their lead in the 32nd minute when Callum Baker escaped a couple of challenges before cutting back for Callum Wilson, who picked out the top corner from 12 yards.
It was almost three before the interval when goalscorers Clarke and Wilson linked up, with the former drilling over from a tight angle.
The pair combined again minutes after half time and on this occasion the ball did go in as Clarke tucked home after being laid in by Wilson.
Coventry should have restored their three-goal advantage but Clarke was unable to complete his hat-trick from a one-on-one opening, shooting too close to George Long.
Chances were coming thick and fast and United should have had their second in the 75th minute when Conor Coady somehow headed over from close range.
They did grab another with 10 minutes on the clock when Taylor again provided the finish from Ryan Hall's delivery.
The Blades were unable to steal a win in the final minutes as Clarke came closest for the home side, rounding Long but seeing his shot cleared off the line.
Three points help Coventry away from the bottom three and up to 16th in the table.