Loic Remy came off the bench to spare Chelsea's blushes at Hull, with goalkeeper Thibault Courtois a relieved man after his first-half howler.
A thrilling 3-2 victory restored the Blues' six-point lead at the Barclays Premier League summit but the Tigers were desperately unlucky not to take something from a rousing encounter.
Fine efforts from Eden Hazard and Diego Costa put the visitors two up inside nine minutes but the expected rout never materialised as Hull stunned their visitors with two goals in as many minutes before the half-hour.
Ahmed Elmohamady tapped home the first after a wonderful run and cross by Andy Robertson and Courtois' calamitous touch handed Abel Hernandez an open net just seconds later.
For long periods thereafter the relegation battlers were the better side, driving relentlessly at a Chelsea team who were visibly shaken, but Remy settled matters just 92 seconds after replacing Costa, who could not add to his 20th of the season.
It was a flowing move from the league leaders, ending with Willian's cutback to Remy, whose shot squirmed agonisingly over the line after sneaking through Allan McGregor's legs.
The result strengthens Chelsea's grasp on the title and does little for Hull's fight against the drop, though Steve Bruce's men at least showed heart for the struggle ahead.
That was not the case when Chelsea took the lead with embarrassing ease in just the second minute.
Hazard was the most alert man on the field, collecting Costa's pass and charging towards goal as the entire Hull team, most notably Gaston Ramirez and Paul McShane, backed away and allowed him to wind up as he approached the area.
His rasping shot zipped past McGregor and kicked off a breakneck period of scoring in style.
Hull should have equalised moments later, Hernandez going one on one with Courtois after Dame N'Doye's clever flick on. He made a clean connection with his shot but Courtois, having narrowed the angle, spread himself to make a vital save.
Chelsea cashed in with their second, Costa collecting Cesc Fabregas' ball before darting into the left channel.
He appeared to have lost his shooting angle but cut back, evaded Michael Dawson and Alex Bruce, and bent a stunning effort across McGregor and in off the far post.
Hull might have crumbled and it briefly seemed certain that they would, but instead they switched from 3-5-2 to 4-4-2 and fashioned a rousing comeback.
The graceful N'Doye worked Courtois with a free-kick then headed the resulting corner straight at the Belgian as Chelsea's back four began to fray at the seams.
Chelsea threatened a third, Costa heading over from Filipe Luis cross, but Hull's appetite only increased.
They needed a moment of inspiration to get on the board and Robertson provided it.
The Scot raced past Willian and Branislav Ivanovic with an electric run down the left then served up a wonderful cross that snaked across the six-yard line and into Elmohamady's path.
His conversion sent the stadium in raptures and just a minute later Hull had their second.
Courtois claimed the assist this time, dealing calamitously with Ivanovic's back pass as he clumsily presented Hernandez with an unmissable gift.
The Uruguayan, having not scored since October, rolled home as the men in Blue looked on in open-mouthed amazement.
For the next 15 minutes Chelsea were on the ropes - Ivanovic, Ramires and Gary Cahill all contributing to a huge error count - but David Meyler and Ramirez sent the best chances well wide.
The visitors were immediately improved after the break - Jose Mourinho presumably having had plenty to say for himself - with Hazard and Costa immediately causing consternation in the Hull defence.
There were signs of nervous tension, though, Costa tustling with Jake Livermore in none too friendly fashion.
Hull were also eyeing three points and Courtois went some way to paying back his debt to the side with a stunning triple save in the 64th minute.
Elmohamady, Livermore and Ramirez all drilled shots goalwards in the space of 10 frantic seconds and each time Courtois was equal to the challenge.
Costa's day ended in apparent discomfort, the striker giving way for Remy.
It proved a precipitous change, with the Frenchman turning match-winner instantly.
Chelsea broke with a precision that had eluded them since the early exchanges and when Willian picked out Remy in the middle a goal seemed certain.
He shot a shade too close at McGregor but with the Scot mid-dive, the ball ricocheted off his legs and over the line.