The Tykes conceded twice in the space of three minutes midway through the first half before Jon Macken pulled a goal back soon after the break.
Substitute Clinton Morrison added a third for the home side in stoppage time yet the scoreline flattered Coventry who were under pressure at regular intervals.
Mark Robins side had started promisingly with defender Stephen Foster striking the bar with a header in the opening few minutes.
But Coventry settled and took the lead after 24 minutes when striker Freddie Eastwood headed in a cross to the far post by Stephen Wright.
Two minutes later, Sammy Clingan doubled the home side's advantage with a volley from the corner of the penalty box following a Michael McIndoe corner.
Robins sent on substitutes Adam Hammill and Iain Hume at the break and it was Hammill who crossed for Macken to reduce the deficit in the 50th minute.
Although both Hume and Hammill went close before the end, Morrison's late header wrapped up three points to lift Coventry within three points of the play-off zone.
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