Thibaut Courtois was indebted to Loic Remy after his late winner extended Chelsea’s Premier League lead over Manchester City to six points.
The visitors went two goals ahead after Eden Hazard fired in and Diego Costa curled in his 20th of the season.
But Hull replied with two goals in 74 seconds as Ahmed Elmohamady slid in before Abel Hernandez took advantage of an error by goalkeeper Courtois.
Substitute Remy then beat Allan McGregor to score with his first touch.
The goal, which sneaked through McGregor’s legs, papered over an inconsistent display from Jose Mourinho’s side, who went from awesome to awful in the space of 28 first-half minutes.
Courtois will be mightily relieved at Remy’s strike after the Belgium goalkeeper failed to control Branislav Ivanovic’s back pass, inadvertently gifting the ball to the onrushing Hernandez for the equaliser.
And the French striker could become an important figure in the title run-in after he replaced the injured Costa, who had a hamstring problem.