Victor Camarasa's 46th-minute effort looked to be securing a huge three points for Neil Warnock's side, but Cesar Azpilicueta levelled the scores in the 84th minute before Loftus-Cheek broke Cardiff hearts late on.
Cardiff will feel hugely aggrieved by the final result, though, with Azpilicueta clearly offside when he headed the away side level six minutes from time.
Pedro had the game's first shot in the 11th minute after finding space outside the Cardiff box, but the Spaniard's attempt just dipped over Neil Etheridge's crossbar.
Two minutes later, Cardiff had an opportunity of their own when Murphy found space inside the Chelsea box, and the attacker's effort only just curled wide of the far post.
Rudiger was next to try his luck from distance as the Chelsea centre-back struck wide of the goal in the 17th minute during an open period at the Cardiff City Stadium.
Chelsea continued to dominate the ball as the first half progressed, but clear chances were few and far between and the 30-minute mark came and went with the score still goalless.
Cardiff did have the ball in the back of the Chelsea net in the 32nd minute when Murphy converted, but the offside flag had been raised and it was indeed the correct decision.
Maurizio Sarri's decision not to select Hudson-Odoi after resting Hazard seemed strange ahead of kickoff, and that argument only strengthened in the first half as Willian and Pedro continued to struggle.
Willian did have the chance to send Chelsea ahead in the 38th minute from a free kick just outside the Cardiff box, but the Brazilian missed the post, before Marcos Alonso turned wide of Etheridge's goal in the away side's final chance of the first period.
Chelsea had 73% of the ball in the first half, but fell behind moments into the second period when Camasara found the back of the net with a quite wonderful finish.
Higuain fired wide of the Cardiff post in the 50th minute before Hazard was introduced shortly after, with Chelsea in desperate need of some magic from their star man.
Hazard's introduction made a huge difference to the away side, but Cardiff were threatening a second as the play developed, with high balls into the box causing Sarri's team a lot of problems.
Loftus-Cheek was next off the Chelsea bench, but there was still no sign of Hudson-Odoi approaching the final 20 minutes of action in Wales.
Willian struck wide of the Cardiff post in the 74th minute, before Olivier Giroud - and not Hudson-Odoi - became the third substitute, with the Frenchman replacing Higuain, which brought a furious reaction from the Chelsea supporters.
The Blues were level in the 84th minute, though, when Azpilicueta headed home from close range. The Spaniard was clearly offside, however, which left Warnock and his team furious.
Cardiff wanted a red card for Rudiger moments later when the defender brought Kenneth Zohore to the ground with a rash challenge, but the colour was yellow.
It was to get worse for Cardiff in stoppage time, though, when Loftus-Cheek headed a deep Willian cross into the bottom corner to secure a huge three points for the away side, who are now just one point off the top four.
Next up for Cardiff is a trip to the champions Manchester City on Wednesday, while Chelsea are back in action at home to Brighton & Hove Albion on the same night.
CARDIFF (4-5-1): Etheridge; Peltier, Morrison, Manga, Bennett; Murphy (Mendez-Laing 90'), Camarasa, Gunnarsson, Arter (Ralls 80'), Hoilett; Niasse (Zohore 85')
CHELSEA (4-3-3): Kepa; Azpilicueta, Rudiger, Luiz, Alonso; Kovacic, Jorginho (Loftus-Cheek 64'), Barkley; Pedro (Hazard 53'), Higuain (Giroud 77'), Willian