Jordan Henderson's wonder-strike condemned Chelsea to their first defeat under Antonio Conte at Stamford Bridge.
The Blues started the match in lethargic form, barely mustering an opportunity before unlikely scorer Dejan Lovren put the visitors in front inside 20 minutes.
It failed to get better for the hosts , and shortly before the break Henderson's sensational strike ended the contest.
A second-half strike from Diego Costa hauled Conte's men back into the contest, though in the end it proved little more than consolation as the Reds saw out the match.
The Blues received an early warning when former striker Daniel Sturridge cut inside and fizzed an effort straight into the arms of Thibaut Courtois, who nearly spilled the shot.
They failed to heed that message, however, and fell behind after 17 minutes when Philippe Coutinho was granted too much space to swing in a cross, which Lovren finished expertly at the far post.
Conte's men looked dazed and failed to muster any clear cut opportunity, instead dealing in a series of ineffective set-pieces.
Indeed it was Klopp's men who looked the likelier to score when Sturridge was released down the left and fired an effort just wide of the far post.
And Chelsea were in double trouble side less than 10 minutes before half-time when Jordan Henderson scored a goal of the season contender.
The 26-year-old picked up on a poor clearance and fired the ball into the top corner of Courtois' net, with the Belgian goalkeeper stranded.
And the Blues started the second half in similar fashion, until Nemanja Matic hauled them back into the match.
The Serbian midfielder made an intricate run into the box, fending off two challenges along the way, before dinking the ball back to Costa, who slotted home.
Costa nearly equalised minutes later when he swivelled and shot in one movement from 20 yards, only for his shot to find the welcoming arms of Simon Mignolet.
Coutinho might have put the game to bed with 12 minutes left, only to see his shot on the turn blocked by Chelsea legs, before substitute Divock Origi forced a fantastic save from Courtois to keep the hosts in the game.
The hosts rallied in the final few minutes, but failed to salvage their unbeaten record for the season.