If Rangers win at Aberdeen tomorrow, the gap will be reduced to two points with three games to go.
However, Hibs were only interested in consolidating third spot so that they could secure a UEFA Cup place and certainly improved their chances with this result.
A first-half goal by Garry O'Connor was cancelled out by substitute Craig Beattie after the interval but late goals by Ivan Sproule and Scott Brown ensured victory for the visitors.
The stadium was half-empty by the final whistle, although Hibs' fans were kept back for ten minutes for their own safety.
Celtic threatened early on when Alan Thompson's quickly-taken free-kick reached Aiden McGeady. The winger's dangerous cross found Bobo Balde but the centre-back was unable to direct his shot on target.
Hibs started boldly with three players up front, and took the lead in the seventh minute with a superb move which swept the length of the park.
From just outside his own penalty area, Derek Riordan's back-heel released Scott Brown who ran half the length of the pitch before finding O'Connor on the edge of the Celtic box. The Hibs striker easily cut inside Stanislav Varga before side-footing his shot into the far corner of the net.
Celtic tried to respond immediately, but the combined strength of Gary Caldwell and Ian Murray blocked Stilian Petrov's shot.
McGeady was frequently losing possession to Steven Whittaker, much to the home crowd's frustration, and switched wings in an attempt to regain some confidence.
Balde missed a great chance to pull Celtic level when he completely missed Thompson's free-kick from only three yards out.
Simon Brown made a great save at the feet of Shaun Maloney from John Hartson's flick as Celtic stepped up the pressure.
McGeady then tried his luck from distance, but his shot was well wide after Maloney's pass had created the chance.
Hibs were still a threat on the break and Antonio Murray's well-struck 18-yard shot was gratefully gathered by Marshall.
Hartson went down in the box as he went for a Thompson cross, but his appeal for a penalty looked half-hearted.
From McGeady's cross, Brown punched clear, but only as far as Balde whose raking shot just cleared the bar.
Thompson's free-kick was deflected into the arms of Brown, as Celtic started to run out of ideas as to how to break down a Hibs defence superbly marshalled by Gary Smith.
The visitors broke swiftly just before half-time, and had a man spare but Amadou Konte's pass to O'Connor was poor and the move broke down. On the stroke of half-time, Hartson chested down a long ball from Jackie McNamara, but his shot only found the side-netting.
Not surprisingly, Celtic replaced the ineffective Maloney with Beattie at half-time, but it was Hibs who nearly scored twice in as many minutes.
Konte cut inside Joos Valgaeren from Derek Riordan's pass, but his shot was deflected for a corner. Then Riordan latched on to a long ball before lobbing Marshall who was well off his line but the Celtic keeper got a hand to it and clawed the ball away for a corner.
Beattie cut inside two defenders before unleashing a shot which Brown did well to hold before McGeady was allowed space to advance, but his shot went high over the bar.
Beattie went down in the box under a challenge by Ian Murray before levelling the scores with a volley from six yards after Petrov's cross had been nodded down by Valgaeren.
With half-an-hour to go, the home fans settled back for what they thought would be an inevitable victory. After Brown dropped Thompson's free-kick, Balde shot into the side-netting before the keeper redeemed himself with a magnificent save from Hartson's flashing header.
Hartson headed wide again, but Hibs gradually got back into the game, especially through their substitutes Dean Shiels and Sproule.
Sproule left Valgaeren for dead and, from his cut-back, Shiels' shot beat Marshall but was cleared off the line by Varga.
Hibs' second goal was only briefly delayed as Sproule slipped his shot home under Marshall from Sam Morrow's flick.
The visitors increased their lead when Antonio Murray's long ball found Scott Brown through on goal and the midfielder struck his shot high into the net from 18 yards.
MAN OF THE MATCH: Gary Smith (Hibernian) - The 34-year-old defender produced a masterly display at the heart of the Hibs rearguard. His rock-like performance laid the foundations for the visitors' shock win.