Matty Godden’s ninth-minute header – helped on its way by poor goalkeeping – was enough to earn the visitors three points.
Against all odds, Coventry are fourth in the table.
Indeed, they utterly deserved this victory against meek opposition, whose fans demanded at full-time the dismissal of head coach Grant McCann.
Despite having made an immediate return to the Championship last season, McCann’s side have won just two league games all season and remain in the relegation zone.
Coventry, by contrast, appear a club going places under Mark Robins.
Buoyed by a raucous away following, they began with the swagger of a top-six team and deservedly made an early breakthrough.
Hull might have felt the initial danger from the impressive Viktor Gyokeres had been snuffed out once Jacob Greaves made a smart block on the right of the penalty area.
But the hosts’ statuesque defence somehow failed to clear their lines, with Ian Maatsen easily finding Godden in a central area inside the penalty area.
Godden’s header was accurate and firm, but Matt Ingram made an awful mess of what should have been a routine parry towards the left of goal.
Things could, and perhaps should, have got better for Coventry soon afterwards.
With Godden allowed time and space to hare through the middle, Ingram partially redeemed himself with a smart stop to his right after 24 minutes.
Hull, with Greaves a one-man barrier at times, at least managed to get to the break without further concession.
Yet with home supporters furious at half-time, there felt little way back for the Tigers – even with just a one-goal deficit.
That sense of hopelessness from the locals was exacerbated by Coventry’s bright start after the resumption which mirrored that of the first half, but did not bring an early goal.
Chances at either side of the pitch were at a premium thereafter, though the need to attack in numbers was, of course, much greater for Hull.
McCann hoped 63rd-minute substitutes Mallik Wilks and Josh Magennis would bring to life a one-dimensional frontline but a tight Coventry defence, expertly captained by Kyle McFadzean, ensured that would never happen.
On 78 minutes, Hull fans once again began chanting in the direction of McCann that he would be “getting sacked in the morning”.
Robins has no such worries as a disciplined Coventry side eased to victory.