McKenna’s side have now won four of their past six games to move into the automatic promotion race after an inconsistent start to the season.
They were dealt a blow pre-match when influential left-back Leif Davis was ruled out through illness.
However, while stand-in Jacob Greaves had an excellent game in his absence it was another change from Boxing Day’s goalless draw at Millwall who stole the show.
Winger Clarke was given a start ahead of Jaden Philogene and regularly created havoc in the Coventry defence in the first half.
The former Leeds and Tottenham man broke the deadlock when defender Cedric Kipre won the ball back high up and played it to Marcelino Nunez to switch it from right to left to Clarke, who drifted inside and then saw his shot loop over Rushworth off Woolfenden.
Clarke was then key to the decisive second goal as he streaked down the left before squaring to Nunez and the Chilean teed up Burns to slide home a second, via a small deflection.
It was a great moment for the Wales international, who only returned from 11 months out with an anterior cruciate ligament injury in Friday’s game.
