The final scoreline was harsh on Accies who took the lead through Marios Ogkmpoe and then performed with admirable resolve after being reduced to 10 men with the first half dismissal of defender Jamie Hamilton.
But Celtic found the ruthless streak necessary to get the job done, inspired by top scorer Odsonne Edouard who claimed a double to take his tally for the season to 22.
Neil Lennon’s men duly took full advantage of Rangers’ latest slip at home to Aberdeen on Saturday with the eight in a row title winners now seven points clear of their Old Firm rivals.
The uncertain start Celtic made to the contest owed much to the contribution of Accies’ goalscorer Ogkmpoe whose physicality and movement was a source of real anxiety to the visitors’ defence in which 20-year-old Stephen Welsh made his first team debut.
It was the more experienced figure of Jullien who was most troubled by Ogkmpoe as the division’s basement side tried to take the game to the champions whenever possible.
Celtic struggled to find their customary fluency in the early stages, although it took a brilliantly timed penalty box challenge from Accies captain Aaron McGowan to deny Edouard what would have been a simple chance in the seventh minute.
Callum McGregor also saw a shot blocked by the home defence, after Leigh Griffiths was unable to get a Greg Taylor cross under control, but much of Celtic’s work lacked conviction.
The home fans were incensed in the 13th minute when Griffiths collected the first caution of the afternoon for an off the ball clash with Sam Woods. The striker appeared to leave a foot in on the grounded Accies player, prompting the angry reaction from the hosts who felt it was a red card offence. Alex Gogic was also booked for his show of dissent to referee Nick Walsh.
A mistake from Kristoffer Ajer presented the lively Ogkmpoe with his first sight of goal in the 21st minute. His powerful first time volley was matched by a fine reaction save from Fraser Forster at the Celtic goalkeeper’s left hand post.
But Forster was left exposed and beaten when Ogkmpoe put Accies in front five minutes later. Scott McMann forced the ball off Welsh for a corner on the left which Blair Alston swung towards the near post. Ogkmpoe escaped Jullien’s tame attempt to block his run and sent a firm header beyond Forster from close range.
Accies’ breakthrough certainly couldn’t be said to have come against the run of play but their hopes of building on it were scuppered by the dismissal of young defender Hamilton 10 minutes before the interval.
The teenager was caught on the wrong side of Griffiths as they challenged for a long through ball from Jullien. Hamilton tugged the striker back on the edge of the penalty area, a rash action as the ball appeared to be running through to goalkeeper Luke Southwood.
It proved to be a case of double jeopardy for the home side as Hamilton was shown a straight red card and Edouard stepped up to brilliantly guide the free-kick over the wall and beyond Southwood’s left hand for his 21st goal of the season.
Edouard missed a decent chance to put Celtic ahead a minute before the break when he lofted a shot over from just inside the penalty area as the visitors looked to press home their personnel advantage.
Accies defended resolutely with Shaun Want, introduced at the expense of David Moyo as the 10 men reshuffled tactically, typifying their determination with a superb block to prevent another chance for Edouard as Celtic upped the tempo in the second half.
The hosts were also riding their luck at times, surviving a couple of penalty claims for handball against Scott Martin and McGowan, while Southwood made a magnificent save when he touched a Griffiths free-kick onto his crossbar.
Accies did occasionally threaten on the counter attack, Ogkmpoe unsettling the league leaders again when he beat Jullien on the right and whipped a dangerous ball across the face of the six yard box which was just too strong for McMann to connect with.
Lennon brought on Ryan Christie and Tom Rogic in a bid to inject fresh creativity to his side in the closing stages and it paid off as Hamilton’s dogged resistance was finally overcome.
Celtic went in front with 12 minutes remaining when Christie’s cross from the left was met by Jullien, the big defender’s foray forward rewarded with a sublime side-foot finish which any striker would have been proud of.
Accies’ race was run and their heads visibly dropped. Celtic took the opportunity to add gloss to the scoreline and boost their already impressive goal difference.
Edouard made it 3-1 when he collected a return pass from Rogic and coolly slid a low shot beyond Southwood, a goal which prompted an exuberant celebration from Lennon who ran onto the pitch.
Having passed up a simple chance to complete his hat-trick when he shot wide from close range, Edouard turned provider in stoppage time with a cutback to Forrest who swept Celtic’s fourth high into the net.