An own-goal by Bobby Thomas in the 12th minute was followed by goals from Ivan Sunjic and Jay Stansfield's 13th of the season.
It clinched Blues' biggest victory since October and only their second win in 11and they are out of the relegation zone after Bristol City denied Huddersfield a win.
Coventry's third defeat in four left the FA semi-finalists Cup six points adrift of the top six with four games left ahead of their big date at Wembley against Manchester United next weekend.
Coventry manager Mark Robins admitted the defeat had effectively wrecked their play-off hopes.
He said: "We had to pick points up in three out of the four games we have lost and you can't do that if you are realistically challenging, so it's massively disappointing.
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