A dogged performance from Motherwell wasn’t enough as Celtic’s clinical edge gave them all three points.
James Forrest, Albian Ajeti and Christopher Jullien were all on target to secure the victory for Neil Lennon’s men.
Manager Stephen Robinson made one change from the starting team which advanced in the UEFA Europa League in midweek. Out from the 5-1 win over Glentoran was Callum Lang, who swapped places on the bench with Tony Watt.
In the face of constant Celtic pressure, the visitors absorbed much of it for large spells in the first half and had the better of the chances on the counter.
The first fell to the unlikely source of Liam Grimshaw. Thriving in a left wing-back role, the Englishman cut inside and sent a low shot bound for the bottom left corner from 25 yards.
Goalkeeper Barkas had to scramble to get across to keep it out, and Long was just short of capitalising on the rebound.
The Steelmen’s resilience would come on the counter attack. After a free-kick was cleared, Celtic roared up the park. With numbers over, Forrest found room facing up against Lamie on the edge of the box, before clipping a shot into the far left corner of the net.
Motherwell continued on undeterred. Watt then had a big chance to level in stoppage time after being picked out at the back post. But his effort went back across the face of goal and was nodded behind for a corner which came to nothing.
The visitors started the second half bright, getting in behind twice early on, but Celtic soon settled into their rhythm.
Chances were kept at a premium, with manager Robinson changing his shape to 4-4-2 with 20 minutes left to try and grab the equaliser.
But it would be Celtic who would get the second goal. A ball in from the left suddenly found Ajeti with too much room in the area, with the substitute powering home into the top left corner despite the last-gasp diving tackle from Grimshaw.
Celtic continued to come in waves. First, Klimala found himself one-on-one with Carson, but the goalkeeper made himself big and saved well with his feet.
Forrest then hit the bar with a dipping shot from outside the box, having cut inside off the left to fire in with his right boot.
Motherwell’s final chance fell to Grimshaw from 25 yards as the game wore to its conclusion. But his placed side-footer was straight at Barkas.
Celtic would make it three in stoppage time. Jullien found himself up the pitch to arrive at the back post and steer home the clincher.
Motherwell: Carson, O’Donnell, Gallagher, Mugabi, Lamie (White 69), Grimshaw, O’Hara, Campbell, Polworth, Watt (Lang 59), Long (Hylton 80).
Subs not used: Morrison, Maguire, Cornelius, Robinson, Seedorf, Hastie.