Leigh Griffiths' 14th goal of the season gave Hibernian their first Easter Road win over Celtic since 2008.
The on-loan Wolves striker gave the hosts an early lead from a tight angle after Paul Hanlon's long ball.
Eoin Doyle should have made it two moments later, but headed straight at Fraser Forster from six yards.
Celtic laid siege on the Hibs goal for the last 20 minutes with home keeper Ben Williams saving brilliantly from Paddy McCourt and Gary Hooper.
Hibernian went into this match having taken a point from the Hoops in a 2-2 draw at Celtic Park in September.
However, Celtic had not lost at Easter Road since a 2-0 defeat in December 2008.
Hibs made Celtic aware of their attacking threat within the opening five minutes, with Doyle and Paul Cairney both driving into the box to fluster the visiting defence.
In the eighth minute, Mikael Lustig had Celtic's first shot on target with a right-footed curling free-kick from 25-yards which Williams held comfortably.
But 60 seconds later Hibs took the lead.
Griffiths nipped in between Thomas Rogne and Forster to latch on to a long ball from Hanlon. His touch took him beyond Forster and from a tight angle he rolled the ball into an empty net.
Georgios Samaras almost replied immediately for Celtic, hitting the post after Lustig's cut-back - but the whistle had gone for offside.
Doyle should have doubled Hibs' lead on 13 minutes, heading Griffiths' free-kick straight into the arms of Forster from six yards.
Former Hibee Scott Brown put a delicious cross into the box for Lassad Nouioui, but the Tunisian could not rise enough to meet the ball.
Efe Ambrose's surging run drew a foul from Gary Deegan, who received a yellow card for the infringement. Nouioui curled the free-kick harmlessly over from the corner of the box.
Doyle's menace continued as he smashed a cross off the arm of Rogne from close-range, but referee Craig Thomson waved away the penalty claims.
And in the 42nd minute, it was again Doyle who gave Rogne a headache, charging down the Norwegian's clearance before blazing a right-foot effort over the bar.
The second half was only a minute old when Lustig put an inviting ball across the six-yard box, although it was just too far ahead of Nouioui and Samaras.
On 56 minutes, Doyle did well on the right by-line to cut back for Griffiths, who in turn teed up Deegan in the box, but his scuffed shot caused no harm.
Swedish international Lustig then collected the ball from Samaras on the edge of the box and looked for Nouioui when he should have shot himself.
With 20 minutes remaining, Hibs captain James McPake came up with a vital headed clearance after Lustig's cross seemed destined for Samaras.
Substitute Beram Kayal should have done better with Hooper's lay-off on 74 minutes, but blasted over.
Victor Wanyama then tried to take matters his own hands with an arrowed shot which had Williams worried on its way over the bar.
The introduction of McCourt gave Hibs' defence more to think about, especially when Williams saved well from the Irishman's thumped effort at the near-post.
In the final 10 minutes, Ambrose's kneed attempt from a corner narrowly missed, then Williams saved expertly from Hooper's deflected shot.
And despite continued pressure heaped on their defence by Neil Lennon's men, Hibs held on to get their first Scottish Premier League win in five games.
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Live Text Commentary
Full Time The game is over, as the referee blows his whistle.88:36
Beram Kayal takes a shot. Ben Williams makes a save.86:42 Substitution
Substitution Efe Ambrose leaves the field to be replaced by Dylan McGeouch.86:05 Substitution
Substitution Danny Handling on for Tom Taiwo.86:05
The ball is crossed by Mikael Lustig, Tom Taiwo manages to make a clearance.84:23
Inswinging corner taken from the right by-line by Emilio Izaguirre.82:50
Gary Hooper takes a shot. Ben Williams makes a save. Corner taken by Emilio Izaguirre from the right by-line, Paul Cairney fouled by Scott Brown, the ref awards a free kick. Lewis Stevenson takes the free kick.80:41
Emilio Izaguirre takes a inswinging corner. Georgios Samaras decides to take a short corner, Ben Williams fouled by Gary Hooper, the ref awards a free kick. Ben Williams takes the free kick.78:30
Patrick McCourt takes a shot. Ben Williams makes a save. Effort from deep inside the area by Gary Hooper misses to the left of the goal.78:17
A cross is delivered by Beram Kayal, clearance by Gary Deegan.76:51
Victor Wanyama has an effort at goal from outside the box which goes wide left of the goal.75:58
Free kick crossed left-footed by Emilio Izaguirre, James McPake makes a clearance.75:58 Booking
Booking Tom Taiwo receives a yellow card for unsporting behaviour.75:42
Foul by Tom Taiwo on Victor Wanyama, free kick awarded.74:32
Patrick McCourt delivers the ball, Paul Hanlon manages to make a clearance.73:17
Shot from just outside the box by Mikael Lustig goes over the bar.71:11
Kelvin Wilson takes the direct free kick.71:11 Substitution
Substitution David Wotherspoon replaces Leigh Griffiths.71:11
Free kick awarded for a foul by Jorge Claros on Beram Kayal.69:39 Substitution
Substitution Beram Kayal joins the action as a substitute, replacing Thomas Rogne.
Corner taken by Emilio Izaguirre from the left by-line played to the near post, save made by Ben Williams.68:43
Centre by Mikael Lustig, Paul Hanlon makes a clearance.68:30
Emilio Izaguirre sends in a cross, Mikael Lustig manages to make a clearance.66:40
Mikael Lustig takes the free kick.66:40 Booking
Booking Booking for Efe Ambrose.66:32
Free kick awarded for an unfair challenge on Efe Ambrose by Paul Cairney.65:05
Free kick taken by Fraser Forster.65:05 Substitution
Substitution Patrick McCourt comes on in place of Lassad Nouioui.65:05
The assistant referee signals for offside against Paul Cairney.61:38
Victor Wanyama produces a right-footed shot from just outside the area that goes wide left of the goal.60:46
Leigh Griffiths has an effort at goal from just outside the box which goes wide of the right-hand post.60:04
Eoin Doyle fouled by Emilio Izaguirre, the ref awards a free kick. Leigh Griffiths takes the free kick.57:52 Substitution
Substitution Tim Clancy leaves the field to be replaced by Alan Maybury.56:47
The ball is crossed by Emilio Izaguirre, Jorge Claros manages to make a clearance.56:31
Georgios Samaras restarts play with the free kick.56:31 Booking
Booking Booking for Tim Clancy.56:20
Foul by Tim Clancy on Georgios Samaras, free kick awarded.55:51
Gary Deegan takes a shot.51:14
The ball is crossed by Scott Brown, clearance by Jorge Claros.49:02
The ball is delivered by Mikael Lustig, save by Ben Williams.47:28
Unfair challenge on Mikael Lustig by Paul Cairney results in a free kick. The ball is delivered by Emilio Izaguirre, Header by Scott Brown from deep inside the penalty area misses to the left of the target.46:48
The ball is swung over by Mikael Lustig.45:41
Lassad Nouioui takes a shot. Save made by Ben Williams.45:01
The second half has started.45:00 +0:07 Half time
Half Time It is the end of the first-half.44:27
Leigh Griffiths takes a inswinging corner from the right by-line to the near post.43:15
Free kick awarded for a foul by Victor Wanyama on Tom Taiwo. Free kick taken by Tim Clancy.41:08
Close range effort by Eoin Doyle goes over the bar.39:56
Georgios Samaras produces a cross, save made by Ben Williams.39:11
Centre by Mikael Lustig, clearance made by Paul Hanlon.37:22
Free kick awarded for a foul by Jorge Claros on Victor Wanyama. Kelvin Wilson takes the free kick.37:15
The ball is swung over by Eoin Doyle, Scott Brown manages to make a clearance.36:07
Foul by Mikael Lustig on Paul Cairney, free kick awarded. Ben Williams takes the free kick.35:59
The ball is swung over by Mikael Lustig, clearance by Paul Hanlon.34:25
The ball is delivered by Georgios Samaras.32:41
A cross is delivered by Emilio Izaguirre, save made by Ben Williams.31:59
Jorge Claros challenges Victor Wanyama unfairly and gives away a free kick. Direct free kick taken by Kelvin Wilson.29:17
Strike comes in from Lassad Nouioui from the free kick.29:17 Booking
Booking Gary Deegan is given a yellow card.29:03
Free kick awarded for an unfair challenge on Victor Wanyama by Gary Deegan.26:50
Georgios Samaras takes a shot. Jorge Claros gets a block in.26:36
The ball is delivered by Jorge Claros.23:25
Tom Taiwo concedes a free kick for a foul on Georgios Samaras. Scott Brown crosses the ball in from the free kick, clearance by Paul Hanlon. Corner from the right by-line taken by Mikael Lustig, Close range headed effort by Thomas Rogne clears the crossbar.22:44
Eoin Doyle takes a shot. Leigh Griffiths gets a block in. Leigh Griffiths is caught offside. Fraser Forster takes the indirect free kick.22:12
Gary Hooper takes a shot. Save by Ben Williams.15:55
The referee blows for offside. Ben Williams takes the free kick.15:02
The assistant referee flags for offside against Leigh Griffiths. Emilio Izaguirre takes the free kick. Unfair challenge on Gary Deegan by Victor Wanyama results in a free kick. Jorge Claros restarts play with the free kick. Free kick awarded for an unfair challenge on Georgios Samaras by Tim Clancy. Direct free kick taken by Emilio Izaguirre.13:36
Gary Hooper gives away a free kick for an unfair challenge on Jorge Claros. Tim Clancy restarts play with the free kick.11:39
Free kick awarded for a foul by Mikael Lustig on Paul Cairney. Leigh Griffiths crosses the ball, Eoin Doyle takes a shot. Fraser Forster makes a save.10:34
Gary Hooper is flagged offside by the assistant referee. Ben Williams takes the free kick.8:50
Lewis Stevenson provided the assist for the goal.8:50 Goal scored
Goal! - Leigh Griffiths - Hibernian 1 - 0 Celtic Leigh Griffiths gets on the score sheet with a goal from inside the six-yard box to the bottom right corner of the goal. Hibernian 1-0 Celtic.6:48
Handball decision goes against Jorge Claros. Shot comes in from Mikael Lustig from the free kick, save by Ben Williams.5:49
Inswinging corner taken by Leigh Griffiths from the right by-line played to the near post, clearance by Thomas Rogne.4:51
Victor Wanyama concedes a free kick for a foul on Paul Cairney. Paul Hanlon takes the direct free kick.0:00
The game begins.
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