It was Scott McDonald who put his former club to the sword with a well taken hat-trick.
A header just before half-time, then a shot which slid past keeper Graeme Smith, before a late penalty were enough for the striker to put Celtic three points clear at the top of the table.
Motherwell went on the attack early on and Celtic keeper Artur Boruc did very well to turn away a swerving 25-yard shot from Ross McCormack.
Then Celtic responded with a Chris Killen shot which was parried out by Smith.
There were worrying signs for the Celtic rearguard when McCormack outpaced John Kennedy, but Stephen McManus cleared his cut back to safety.
Smith produced a marvellous save with his feet to keep out Killen's header from Shunsuke Nakamura's corner.
Boruc was careless with a pass intended for Lee Naylor but the keeper recovered to touch away Steven McGarry's net-bound shot.
Nakamura's pass found Scott Brown at the edge of the area and, after somehow wriggling his way past two defenders, his well struck shot was saved by Smith diving to his left.
Then Mark Reynolds did well to beat Killen to McDonald's lay-off before Smith again blocked Gary Caldwell's header with his legs.
It always looked as though a set-piece move would see Celtic take the lead and so it proved as McDonald stooped low to bullet his header home from Nakamura's corner.
Motherwell could have fallen two behind before the break but Killen somehow hit the post with the keeper stranded.
After the break, Aiden McGeady's curling shot from 20 yards came back off the bar.
Motherwell threatened when McCormack's released Chris Porter but the striker's shot was blocked by Boruc.
Celtic increased their lead when Naylor's pass put McDonald through and the stocky striker coolly slid his shot past the keeper.
McDonald notched his second hat-trick of the season after Stephen Craigan tripped him in the penalty box and he sent Smith the wrong way with the resultant spot-kick.