A goal in each half from John Hartson and Alan Thompson gave Celtic their 16th straight SPL win to extend their lead over Rangers at the top of the table to eight points, yet things might have been different had it not been for keeper Rab Douglas.
The Scotland number one has endured his fair share of criticism for both club and country and is being linked with a move away from Parkhead, but his first-half penalty save from Derek Adams proved a pivotal moment at Fir Park.
Celtic's opening goal owed as much to their medical staff as their players as Hartson and Chris Sutton both shrugged off pre-match injury worries to combine slickly in the third minute.
Sutton peeled away from his markers on the left and whipped in a low cross, which Hartson tucked away from inside the six-yard box.
The Hoops duo soon had chances to double their team's lead but Hartson headed tamely at keeper Gordon Marshall before Sutton rippled the side netting with a left-foot effort.
Celtic's first anxious moment came in the 22nd minute as a cross from Stephen Pearson eluded Douglas and had to be cleared by defender Johan Mjallby.
Motherwell kept up the pressure and Adams twice went close from free-kicks, the first coming back off the post and the second flashing narrowly wide.
Adams was handed the perfect opportunity to equalise after 28 minutes following Mjallby's trip on David Clarkson, but his spot-kick was brilliantly saved by Douglas.
The visitors looked even more vulnerable when top scorer Henrik Larsson went off with a recurrence of a back injury, only for Thompson to make the points safe with a stunning second goal 19 minutes from time.
Stilian Petrov laid the groundwork by winning a free-kick from defender Stephen Craigan and Thompson did the rest with a swerving left-footed strike from 20 yards out.