Two Leigh Griffiths goals were sandwiched in between a Scott McDonald strike for the Well, meaning Ronny Deila's men took full advantage of Aberdeen's defeat at Hearts on Friday night.
This win will have given the league leaders a major confidence boost going into next week's Scottish Cup semi-final against Rangers at Hampden Park.
Mark McGhee's Motherwell went into the match very much as the on-form side, and didn't change his starting 11 from last week's last gasp win at Inverness. For Celtic, Charlie Mulgrew replaced injured Erik Sviatchenko and Colin Kazim-Richards started out on the left in a 4-3-3 formation.
Celtic dominance eventually pays off
Celtic started brightly and had the lion's share of possession, peaking at 67% in the opening 10 minutes. Griffiths passed up two chances early on but was tenacious throughout to get back into scoring form.
Motherwell keeper Connor Ripley was the star of the show in the first half, denying Griffiths several times from point-blank range and had to be extra strong to deny Kazim-Richards.
The English stopper would have thought his biggest challenge of the match would to be deny Griffiths from the penalty spot. Celtic were given a spot kick following a trip on Patrick Roberts at the edge of the box by Morgaro Gomis. Fortunately for the Steelmen, Griffiths continued his hopeless penalty record as he sent the ball low and off-target against the advertising board.
Ripley guessed the correctly, but the taker has now only scored three of his last eight penalties.
A minute before the break and Celtic did go in front with Griffiths making up for his earlier penalty miss. Tireless work by Kieran Tierney down the left flank allowed the young full-back to drive a low cross to the centre of the box and Griffiths to volley in.
Home side put up a fight but cannot hold on
In the second half Motherwell put up a much sturdier fight as their fantastic run of wins were in danger of ending. Louis Moult, who had been quiet for large parts of the first half, forced Craig Gordon into action early to stop his cut-back.
Then, 10 minutes from the restart, Motherwell thought they had restored parity through McDonald, following some smart and quick play down the left. However, the Australian striker was correctly flagged to be a half-yard ahead of play when he tapped in from a few yards out.
Nevertheless, the ex-Celtic striker McDonald continued in his search for a goal and managed to grab it five minutes after the offside call. In a similar fashion to Griffiths' opener, McDonald received the ball in the centre and swept the ball into the corner of the net.
As the game was drawing closer to its finish, careless mistakes started to appear in the Steelmen's back line. Griffiths almost capitalized in one instance, but only had to wait a few minutes later before scoring the winning goal. Another ball to the centre of the box allowed Griffiths, once again, to directly hit on-target. Unfortunately for Ripley, the ball went through his arms to gift Celtic the winning goal.
At full-time there was a bit of controversy with both managers at the handshake. Motherwell manager McGhee snubbed his opposite number Deila after the whistle and later said there was no story in the incident. However, the McGhee would later state that he thought Deila blanked him earlier in the match but turned out to be a misunderstanding.