Johnny Kenny opened scoring in the 10th minute with his fourth goal in four matches under interim manager Martin O'Neill as the William Hill Premiership champions cut the gap on leaders Hearts to seven points with a 4-0 victory over Kilmarnock.
Kieran Tierney was also among the scorers with his first Celtic goal in seven years.
The left-back, who scored on his final Arsenal appearance in May, drilled a powerful angled shot from 25 yards to double Celtic's lead six minutes into the second half.
It was the 28-year-old’s first Celtic goal since a Europa League win over RB Leipzig on November 8, 2018.
Daizen Maeda missed several good chances for Celtic and Kilmarnock hit the crossbar through Bruce Anderson before Tierney struck.
They initially struggled to build on the cushion but late goals from Maeda and substitute Arne Engels, from the spot, added a flattering sheen to the scoreline.
Both teams went into the contest on the back of difficult periods.
Killie had conceded 10 goals in four consecutive defeats while Celtic’s Europa League defeat against Midtjylland was followed by an escalation of tension between the board and a section of fans.
The Green Brigade were effectively issued with a six-match ban over an incident involving police and stewards at Celtic’s previous home match and there were a number of empty spaces in the standing section.
There was still a vocal group there who led Remembrance Day protests against what was described over the public address system as a "moment’s silence" to remember those who had died in conflict, including several named Celtic players who had died in the First World War.
There were loud boos and whistles before Don Robertson quickly blew his whistle as fans who had turned their back on the pitch began singing a song about the death of Aidan McAnespie, who was shot by a British soldier at an Army checkpoint in County Tyrone in 1988.
Celtic handed a debut to on-loan Manchester City defender Jahmai Simpson-Pusey, who delivered a solid performance at right-back after a slightly nervy start.
Celtic were quickly on top. Maeda shot over the bar from a decent chance before Kenny hit an opportunist strike off the inside of a post.
The Irishman was soon on target, knocking home Reo Hatate’s cutback from close range after a costly slip by Robbie Deas as the defender looked set to deal with Marcelo Saracchi’s forward pass.
The Argentinian left-back soon joined Celtic’s injury list and was replaced by Tierney.
Maeda made a mess of an open-goal opportunity after Eddie Beach spilled a shot from Sebastian Tounekti and Killie twice threatened before the break.
Anderson volleyed off the bar from a tight angle after latching on to a long ball and Scott Tiffoney’s strike was deflected over following David Watson’s break.
Maeda headed over before Kilmarnock paid the price for standing off Tierney.
Killie kept plugging away but could not carve out a clear chance and Maeda removed any doubt about the outcome in the 85th minute with his fourth goal of the season.
The Japan striker swept the ball inside the near post following a long-range through ball by substitute Engels.
The Belgium midfielder then converted a penalty in stoppage time after James Brown pulled back Yang Hyun-jun.
Elsewhere, Hearts were held 1-1 at home by Dundee United, their second draw in three matches.
Alexandros Kyziridis' shot rebounded off a post and ricocheted over the line off United keeper Yevheni Kucherenko only for Luca Stephenson to equalise just before half-time.
New Rangers manager Danny Rohl enjoyed a third successive league victory with a 3-0 win over Dundee moving them to within 12 points of leaders Hearts with a match in hand.
Nico Raskin headed home a ninth-minute corner and the lead was doubled by Mikey Moore’s first goal since joining on loan from Tottenham before Djeidi Gassama curled home the third in the 90th minute.
Motherwell made it three unbeaten in the league with a 1-1 draw at Aberdeen, Elijah Just cancelling out Jesper Karlsson’s opener for the hosts.
