Gary Hooper gave Celtic a 40th-minute lead but the hosts struck seconds before the break when Keith Lasley beat Thomas Rogne to a loose ball and played a through pass to Henrik Ojamaa, who kept his composure as he raced towards goal and drilled past Fraser Forster.
Michael Higdon (50) turned the game in favour of the Steelmen with a confident penalty after Charlie Mulgrew was unfortunate to collide with Ojamaa.
Five minutes later Tom Hateley sent a hanging delivery into the box where Mikael Lustig attempted to clear behind, but his header hit the post and the ball spun off Forster's back and over the line.
Motherwell should have taken an early lead when Hateley played a short corner to Nicky Law and he delivered a dipping cross into the six-yard box, where Shaun Hutchinson flicked the ball past the post.
Darren Randolph then produced a wonderful save when Georgios Samaras flicked the ball to Tony Watt and his curling delivery found Hooper at the back post, but his cushioned volley was blocked by the keeper.
But Randolph was caught out by the pace of Watt who also left Simon Ramsden behind as the youngster raced towards the penalty area and flicked the ball to the unmarked Hooper, whose header hit the bar before he turned and swept the rebound into the net.
Lustig almost deflected a Chris Humphrey shot into the net but Forster clawed the ball away, and the big keeper later thwarted James McFadden on another Motherwell break.
Tony Stokes hit the post in the dying seconds for Celtic with the ball spinning away from Hooper and Watt, but the visitors never recovered from Ojamaa's goal as Motherwell booked a place in Europe for next season.