Goals from Anthony Stokes and Kris Commons, coupled with St Johnstone's demolition of Inverness in Perth, sent the Hoops three points clear with a game in hand.
Celtic took the game to Stuart McCall's visitors from the off but were dealt a blow in the ninth minute when wing-back Adam Matthews was stretchered off following a crunching tackle by Well skipper Keith Lasley.
James Forrest replaced the Welshman and saw an early chance go wide before a blunder from keeper Lee Hollis allowed Stokes to fire the champions ahead in the 21st minute.
The Englishman completely misjudged a flick-on from Commons and with the ball loose in the box Stokes pounced to shoot into an empty net.
Hollis made amends with a fine save from Commons in the 34th minute but he was powerless to prevent the same player adding a second shortly after the break.
An error from Ian Vigurs let the midfielder in on goal and after nut-megging former Celtic defender Stephen McManus, he rode a tackle from Lasley before clipping the ball over the on-rushing Hollis.
With just five minutes left, Celtic's in-form keeper Fraser Forster prevented what looked a certain goal when clawing a John Sutton header off the line in Motherwell's only clear-cut chance of the second period.