The visitors were well in control of the first half and created plenty of chances as Clarke fired over from the edge of the box and Callum Wilson blazed over from close range early on.
Connor Thomas was next to go close after 17 minutes when his low strike took a wicked deflection and was kept out by a fine save from Stevenage goalkeeper Chris Day.
Coventry finally took a fortuitous lead after 33 minutes when Stevenage winger Robin Shroot's lazy back pass put Clarke clean through and the Sky Blues skipper thumped the ball beyond Day.
The visitors continued to dominate in the second period and had a decent shout for a penalty turned down when Wilson went down under Jon Ashton's challenge after being put through by Clarke.
Ashton nearly grabbed a shock equaliser late on but his low shot was well blocked by Coventry 'keeper Joe Murphy.
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