An early goal from Tony Stokes was all Celtic had to show despite dominating the entire match, in which Motherwell played out the final 25 minutes with 10 men after Simon Ramsden was sent off for a late challenge on James Forrest.
Stokes struck on six minutes when Stefan Johansen pounced on a slack pass-back from Fraser Kerr and rounded Dan Twardzik before laying the ball back for the Republic of Ireland international to fire home from eight yards.
The league leaders could have scored after only two minutes when Scott Brown turned brilliantly just inside his own half and split the Motherwell defence with a pass to John Guidetti, who took the ball in his stride but sent his low shot just wide of the post.
And the visitors created another opportunity on 13 minutes when Brown stepped over a square pass from Nir Bitton across the front of the penalty area allowing Forrest to stride into the box and send his drive narrowly wide of the same post.
Seven minutes later Johansen burst forward from the centre circle and threaded the ball to Bitton, whose reverse pass was returned to the midfielder via the heel of Guidetti but the Norwegian shot straight at Twardzik.
And Celtic should have doubled their lead when Johansen drifted in from the right flank and slipped a pass into the box for Guidetti to net with a bicycle-kick, only for the striker to be erroneously flagged offside by the far side assistant.
Motherwell survived another scare when a cross from right-back Adam Matthews was turned behind for a corner by the raised hand of Zaine Francis-Angol, but no penalty was awarded.
After the break Matthews picked out Forrest with a square pass and the Celtic winger skipped past two defenders before testing Twardzik with a shot from 20 yards, which the keeper got down to hold.
Motherwell were reduced to 10 men when Ramsden brought a flowing Celtic move to an end by going through Forrest.
Celtic squandered another opportunity when Johansen slipped a weighted pass to Emilio Izaguirre but the left-back hooked the ball over the bar after Twardzik blocked his first effort.
Either side of that Twardzik denied Guidetti, when a square pass to Forrest may have been a better option, and then the Swede clipped the ball wide with the goal at his mercy.
Twardzik again denied Celtic when he blocked a close-range effort from Forrest as Celtic continued to pound the Motherwell defence.
But Motherwell missed a glorious chance to snatch a point seven minutes from time, with their only opportunity of the game, when Lionel Ainsworth clipped the ball into the penalty area and the unmarked Lee Erwin planted his header wide from seven yards.
And Erwin blotted his copybook in added-time when he threw himself into Efe Ambrose in an attempt to win a penalty, but was given a yellow card for simulation instead.