Kris Commons opened the scoring with his 20th goal of the season in the eighth minute but the champions had goalkeeper Fraser Forster to thank for keeping Hibs at bay with several good saves - the best from Sam Stanton in the second half - as Terry Butcher's men fought their way back into the match.
However, a brilliant free-kick from Dutch defender Virgil van Dijk in the 76th minute sealed the Hoops' 12th straight domestic victory.
Substitute Teemu Pukki, on at the interval for Nir Biton, put some gloss on the scoreline with a terrific drive eight minutes from time before Commons scored with a penalty after Hibs defender Alan Maybury had fouled Pukki.
The statistics keep mounting in the Parkhead club's favour.
The win took Celtic 15 points ahead of second-placed Aberdeen with two games in hand over the Dons, and they also racked up their 10th domestic clean sheet as they stride over the horizon.
Hibs wide man Alex Harris had the first effort of the game in the second minute with a drive from 20 yards which just missed the target but that only offered false optimism to the home supporters who watched their side hand the visitors the lead.
Commons had a good chance in the fifth minute after Hibs defender Jordon Forster passed straight to Hoops striker Georgios Samaras - in for the suspended Anthony Stokes - who quickly sent the former Nottingham Forest and Derby player through on goal.
However, Commons slipped just as he was setting himself to shoot and the opportunity was gone, but another was only minutes away and came courtesy of another defensive blunder.
Forster and fellow centre-back Michael Nelson both went for a header with the ball falling kindly for the Celtic player, who took it on before firing confidently past home goalkeeper Ben Williams.
There was a Hibs appeal for a penalty when striker James Collins went down in the box under a challenge from Van Dijk but referee Craig Thomson was unimpressed.
The match was error-strewn but Hibs had the chance to level in the 19th minute when a deep cross from Harris found Nelson unmarked at the far post but his header from eight yards went straight into the arms of Forster.
Just before the half-hour the England cap was called into action again when he had to save a decent drive from Stanton with Celtic defender Emilio Izaguirre completing the clearance.
Forster again came to Celtic's rescue after the break with two saves in a minute from Abdellah Zoubir.
His first came in the 56th minute when he clawed away a long-distance strike which was heading for the top corner, before moments later diving low to his right to block Zoubir's drive for yet another corner which came to nothing.
At the other end, a dipping volley from the edge of the box from Celtic skipper Scott Brown was held confidently by Williams.
However, Forster produced the best save of the match in the 66th minute when he flew to his left to push a goal-bound drive from Stanton past the far post.
Play stretched further in the closing stages but Celtic wrapped up the points after Nelson handled a pass from Pukki, allowing Van Dijk to step up and curl the 25-yard free-kick past the helpless Williams.
Pukki compounded Hibs' misery in the 82nd minute by driving high past Williams from 16 yards for number three.
There was time for new signing Stefan Johansen to make a late Celtic debut, replacing Charlie Mulgrew, before Maybury conceded a penalty with a challenge on Pukki, allowing Commons to hammer in the spot-kick for goal number 21 of the season.