Liam Cooper’s unfortunate 13th-minute headed own goal, in what was the 20-year-old Scot’s first league game for the Tigers since August 2010, handed the visitors the initiative before substitute Cody McDonald’s late finish.
Coventry, now unbeaten in six and having recorded back-to-back wins for only the second time this season, are hitting form at just the right time as the campaign reaches its climax.
Alex Nimely hit the angle in the first half before being denied by a great last-ditch challenge in first-half stoppage time from Hull skipper Jack Hobbs, who was injured in the process.
Hull struggled to really get going and Aaron Mclean was fortunate to avoid a second booking following a nasty second-half tackle on Richard Keogh.
It was a fourth successive defeat for the Tigers, who have seen their play-off charge hit the buffers and are now five points adrift of the top six.
Coventry started what was an open encounter firmly on the front foot, displaying plenty of confidence, although it was Hull who fashioned all of the early chances.
Mclean glanced a header wide before Murphy was called on to deny both Matty Fryatt and Robbie Brady with good saves.
With the game flowing from end to end it was the Sky Blues who broke the deadlock in fortuitous circumstances.
Keogh’s header from Sammy Clingan’s free-kick was well parried by Vito Mannone but Cooper panicked and headed the rebound into his own net.
Fryatt lashed an effort narrowly off target as the hosts looked for an immediate route back into the game.
The former Leicester forward fired over again in the 36th minute before Nimely saw an effort, which appeared to be relatively harmless, clip the angle.
Cameron Stewart brought a save from Murphy while Gary McSheffrey tested Mannone at the other end in what was an entertaining close to the first half.
But it was Nimely who enjoyed the best opening in stoppage time when he found himself clean through only to be denied by a great challenge from Hobbs.
The tackle, however, came at a cost as Hobbs, who required treatment immediately after, was forced off at half-time.
That handed a league debut to Sonny Bradley who, alongside Cooper, provided Hull with a vastly inexperienced central defensive partnership.
Liam Rosenior saw his 56th-minute effort blocked by Martin Cranie while Oliver Norwood put wide at the far post as Coventry threatened.
Mclean was extremely lucky to avoid a second yellow card for a dangerous challenge on Keogh, before then testing Sky Blues stopper Murphy soon after while Fryatt also hooked just over.
Coventry sub McDonald forced a solid save from Mannone before sealing the points with a super strike across the Tigers goalkeeper in the 86th minute.
It capped a disappointing five days for Hull, who have lost 2-0 to struggling Portsmouth and now Coventry.