Second half goals from Ivan Sproule and Scott Brown gave Hibernian their first win at Celtic Park for 13 years, throwing the title race wide open.
Scott Brown is mobbed by his team-mates
Garry O'Connor opened the scoring after six minutes, sending a low shot past David Marshall from eight yards.
Substitute Craig Beattie volleyed in the equaliser after 59 minutes.
Substitute Ivan Sproule fired Hibs ahead in the 79th minute before Scott Brown chipped Marshall for the third two minutes later.
Celtic got off to another bad start as the Edinburgh side followed the recent examples of Aberdeen and Hearts by snatching an early lead.
Derek Riordan started the move with a clever back-heel deep in his own half to send Scott Brown away into the opposition's half where he found the overlapping Garry O'Connor.
The striker still had plenty to do, but cut inside Stanislav Varga with ease and then placed his right-foot shot past the on-rushing David Marshall from eight yards in the seventh minute.
Bobo Balde squandered a glorious chance to level the scores in the 18th minute after Steven Whittaker had conceded a free-kick for a clumsy foul on Valgaeren.
Alan Thompson swung in a trademark left-foot cross and the Hibernian defence gave the defender a free header, but Balde completely missed the ball.
Hibernian looked threatening on the break and Antonio Murray tested Marshall with a low drive in the 29th minute, but the youngster saved comfortably under pressure.
Celtic were let off the hook in the 48th minute when Amadou Konte got behind the defence and his left-foot shot was deflected just wide off Valgaeren.
Moments later and the home side had Marshall to thank for denying Hibernian a second goal following a rare mistake by Neil Lennon.
Riordan seized on the ball and tried to lob the young goalkeeper from 22 yards but he raced off his line and threw his hand up to touch the ball just past the upright.
Celtic hauled themselves back on level terms on the hour thanks to a great opportunist strike from Beattie.
Petrov clipped the ball into the box and the youngster pounced on Valgaeren's knock-down to drive a right-foot volley past the hand of Simon Brown from six yards.
Hibs were now feeling the heat as the home fans and their heroes turned up the temperature.
It clearly got to Brown in the goal after 62 minutes as he spilled a Thompson free-kick but he breathed a sigh of relief as Balde smashed the loose ball into the sidenetting.
Nearly everybody in Celtic Park thought Hartson had headed Celtic into the lead in the 67th minute but Brown threw himself to his left to save his effort from Thompson's cross.
Substitute Ivan Sproule became the hero with 11 minutes remaining, when he pounced on a loose ball to fire under the body of Marshall before substitute Sam Morrow, on for O'Connor, was booked for celebrating.
But there was even more drama moments later when Brown took Murray's long ball in his path and coolly chipped Marshall to spark more wild celebrations in the visiting section.
Beattie tried to pull his side back into the game with two minutes left but Brown pushed his shot over the top and the famous success was secured.
Celtic: Marshall, McNamara, Balde, Varga, Valgaeren, Petrov, Lennon, Thompson, McGeady (Wallace 69), Hartson, Maloney (Beattie 45). Subs Not Used: Douglas, Henchoz, Sylla, Lambert, Laursen.
Goals: Beattie 59.
Hibernian: Simon Brown, Scott Brown, Caldwell, Konte (Shiels 72), Glass, Antonio Murray, Ian Murray, Smith, Whittaker, Riordan (Sproule 71), O'Connor (Morrow 77). Subs Not Used: Alistair Brown, Hogg, McDonald, Murphy.
Booked: Glass, Morrow, Shiels.
Goals: O'Connor 7, Sproule 79, Scott Brown 81.
Ref: K Clark