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.