Chelsea ran into a 2-0 lead within nine minutes through Eden Hazard’s 25-yard strike and Diego Costa’s fine finish from an angle.
But two quick-fire goals from Hull brought them level before the break, Ahmed Elmohamady turning home from close range before Thibaut Courtois’ poor touch allowed Abel Hernandez to net the equaliser.
Despite Hull going close on several occasions in the second half, substitute Remy grabbed the winning goal from 12 yards just two minutes after coming on.
The result keeps Hull three points clear of the drop zone with eight games to play, while Chelsea stay top by six points over Manchester City with a game in hand.
Chelsea had won just two of their last six games in all competitions going into the clash, while Hull had lost just one of their last six in the league.
But the Premier League leaders were ahead after just 79 seconds through Hazard, who collected the ball 45 yards out and drove forward before unleashing an unstoppable left-footed effort past Allan McGregor.
Hull were nearly level just minutes later, but Courtois stood tall to keep out Hernandez after the Hull striker was put through on goal.
Chelsea went 2-0 up on nine minutes through Costa, curling home from an angle after being found on the left by Cesc Fabregas.
Dame N’Doye tested Courtois again with a curling 25-yard free-kick, but the hosts halved the deficit and were then level with two goals in two minutes.
First, Elmohamady turned home from six yards after being found by a fine ball across the face of Courtois’ goal on 26 minutes.
Then, Courtois’ calamitous heavy touch from a Branislav Ivanovic back pass fell kindly to Hernandez, who slid into the empty net from 10 yards.
Hull continued for the rest of the first half on top, posting 16 shots on Chelsea’s goal as they looked to complete a fine comeback before the break.
Chelsea looked more assured in defence in the second half, and nearly went ahead just five minutes in through Fabregas, but the Spaniard’s effort across goal fell a yard wide.
Courtois made up for his earlier mistake with a fine triple save with 25 minutes remaining, keeping out Elmohamady and Jake Livermore’s resulting rebound, before tipping over Gaston Ramirez’s effort as the ball bounced to the midfielder inside the area.
Remy entered the field with 75 minutes on the clock to replace Costa, who was seen holding and stretching his hamstring, and the Frenchman made an instant impact two minutes later.
Collecting Willian’s centre, Remy’s effort from 10 yards squirmed under McGregor’s grasp to give Chelsea all three points.
Hull: McGregor (5), Bruce (6), Meyler (6), McShane (6), Dawson (6), Livermore (6), Ramirez (7), Robertson (7), Elmohamady (7), N’Doye (6), Hernandez (6)
Subs: Brady (5), Aluko (5), Quinn (5)
Chelsea: Courtois (5), Ivanovic (5), Cahill (5), Terry (5), Filipe Luis (6), Fabregas (5), Matic (5), Ramires (5), Willian (6), Hazard (7), Diego Costa (6)
Subs: Zouma (5), Oscar (5), Remy (7)
Man of the match: Eden Hazard