With Rangers facing a tough trip to Aberdeen on Sunday there must be every chance that the current gap will remain.
Celtic never had to extend themselves against a Motherwell side who played without confidence and belief after their recent poor run.
After Stilian Petrov made the initial breakthrough just after the half-hour mark, the match was over when Chris Sutton netted early in the second period.
This allowed Bhoys boss Martin O'Neill to send on Juninho for the last 20 minutes, after the Brazilian was again dropped to the bench.
The home side applied some early pressure, and from John Hartson's pass Petrov forced a corner - but Ulrik Laursen could only head over from Alan Thompson's delivery.
Another clever flick by Hartson released Aiden McGeady, but the visitors' defence just managed to crowd him out, at the expense of a corner.
Motherwell nearly surprised Celtic with a well-worked move at their first corner. Kevin McBride's quickly taken flag-kick found Scott McDonald unmarked at the edge of the box but the striker's shot, though well-struck, was just off-target.
Petrov threatened down the right flank, but Stephen Craigan at the heart of the Motherwell defence was coolness personified as he chested the ball back to keeper Gordon Marshall.
Jackie McNamara then did well to tackle David Clarkson after Bobo Balde's poor pass threatened to leave his defence in trouble.
Celtic should have taken the lead when Hartson's blocked shot fell perfectly for Sutton, but Marshall made a brave point-blank save from the striker's shot.
Motherwell briefly threatened when Craigan got on the end of McBride's corner at the near-post, but his header floated wide.
McGeady then skilfully skipped past Steven Hammell, but Marshall was again well positioned to parry his effort.
Celtic made the breakthrough after Hartson won possession in midfield. The Welsh striker's pass found Sutton, who in turn released Petrov and after riding a strong tackle from Paul Quinn the midfield player's shot had sufficient power to find the corner of the net, despite Marshall's despairing touch.
Just before half-time McGeady set off on another exciting run, but his cross-shot was deflected into the arms of Marshall.
Celtic looked keen to finish the match off at the beginning of the second-half. From McNamara's free-kick Stanislav Varga touched the ball on, but Balde's effort was deflected for a corner.
A clever back heel from McGeady found Sutton, but his pass to Hartson found the striker in an offside position.
Neil Lennon did well to intercept Scott McDonald's run and usher the ball back safely to Robert Douglas before McNamara headed clear Hammell's dangerous cross at the back post.
When Celtic's second goal did arrive, it was after a dreadful mistake by McDonald in the centre circle. The Australian carelessly conceded possession to Thompson, leaving his midfield stranded.
Thompson took full advantage by threading a superb ball through to Sutton, who curled his shot around Marshall and just inside the post.
Marshall then had to hack clear a poor Hammell pass-back with Sutton bearing down on him.
Douglas did not have to do much to gather Jamie Paterson's weak shot which summed up the poverty of Motherwell's outfield play, as it was their only effort of the second-half.
The Bhoys' dominance allowed O'Neill time to send on Juninho and Henri Camara, but the points had been wrapped up long before then.
Man of the Match: Chris Sutton
The former Chelsea man produced a typical performance combining steel and flair and fully deserved his decisive goal.