Indeed if Motherwell's finishing had matched some of their build-up play, this could have been an embarrassing result for the home team.
As it was substitute Derek Riordan's goal just after the break was sufficient to see Celtic edge nearer to the title.
Should Rangers lose tomorrow, then Celtic will have won the SPL title.
Celtic started off brightly and Maciej Zurawski should have done better than pull his shots wide from two early chances. Motherwell, with some neat midfield possession, came more into the match, with Dave Clarkson giving Steven Pressley and Darren O'Dea a troubled afternoon.
Keeper Graeme Smith did well to block Paul Hartley's header with his legs, but the Steelmen also went close through efforts from Krisztian Vadocz and Clarkson.
If Clarkson on the six-yard line had got a touch to Brian Kerr's shot from outside the box, the visitors could have gone ahead at half-time.
Celtic finally made the breakthrough just after the interval when Shunsuke Nakamura's cross was nodded down by Jan Vennegoor of Hesselink for Riordan to force the ball home from six yards.
Smith then produced a fine save from Nakamura before Artur Boruc did likewise to deny Darren Smith and a Kerr shot was deflected on to the roof of the net.
Celtic were hanging on for the final whistle. Vadocz nearly wriggled his way through and Kerr volleyed wide, but Motherwell could not get the goal their play deserved.