The Steelmen were looking to strengthen their chances of finishing third and securing a UEFA Cup place, but were undone by two second-half strikes from the Bhoys.
The first half was a surprisingly poor affair which was littered with mistakes and spoilt by erratic refereeing.
The referee was actually first in action when he chose to take no action when Barry Robson appeared to throw Motherwell's David Clarkson to the ground off the ball.
Goalmouth incidents were few and far between, although both sides did have long-range efforts from Keith Lasley and Andreas Hinkel which sailed wide.
The only effort on target came after a fine run down the right by Darren Smith, but his shot was met tamely by Marc Fitzpatrick and allowed Artur Boruc to save easily.
The second half started in similar fashion, until just after the hour mark when the game finally burst into life.
Motherwell took the lead on 60 minutes when a Brian McLean cross from the right was floated perfectly for Chris Porter to climb over Bobo Balde and head home his 16th of the season.
Within a minute Celtic were level and once again it was a perfect cross which set up the chance.
Shunsuke Nakamura lifted the ball into the box from the right and Scott McDonald rose unmarked to head past Luke Daniels.
Celtic took the lead with 11 minutes left in slightly controversial fashion as Balde appeared to head a cross wide, but the officials somehow saw it as a corner to the visitors.
From the resulting kick, Robson delivered a perfect in-swinger for Georgios Samaras to head home from close range.
Towards the end of the match the referee had to visit the home technical area to calm down the Motherwell management team, who were clearly upset by the award of the corner leading to the goal.
But that made no difference to Celtic, who held on to take three points and keep the pressure on Rangers ahead of their game at Hibs on Sunday.