Derek Riordan came off the bench to secure a victory that takes Celtic to within three points of retaining the Scottish Premier League title.
Fit-again Maciej Zurawski had been preferred to Riordan and missed a couple of chances before hobbling off injured after 33 minutes.
Motherwell had matched their hosts and frustrated the home crowd.
But Riordan fired home following a fine breakaway and Celtic comfortably held on for victory.
Motherwell boss Maurice Malpas had carried out his threat to drop his top scorer, Scott McDonald, feeling it unfair to field the striker against the club he will be joining in the summer.
Also missing were Jim Paterson and Paul Keegan, with Steven McGarry, David Clarkson and Kevin McBride coming into the starting 11.
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Zurawski had returned to the Celtic starting line-up in place of Craig Beattie as manager Gordon Strachan looked for more goals from his strikeforce.
But the Pole skewed his left-footed drive from 12 yards wide of the target as the home side created the first chance.
Zurawski fired wide again moments later, this time from a more acute angle on the right side of the penalty area.
Motherwell midfielder Krisztian Vadocz drove wide from the edge of the Celtic box when he ought to have tested Artur Boruc as the visitors came more into the game.
An air of disgruntlement inside Celtic Park seemed to inspire the visitors who appeared to slowly grow in confidence as Vennegoor of Hesselink prodded another chance wide.
Motherwell skipper Stephen Craigan was booked for a 33rd-minute foul on Zurawski that led to the Pole limping off to be replaced with Derek Riordan.
The appearance of the former Hibernian striker lifted the crowd momentarily and seconds later McGeady hit the side netting with an angled drive.
But the visitors threatened again, Clarkson forcing Boruc on to his toes to save his right-footed curler from 20 yards.
Celtic made the breakthrough on the counter-attack after 52 minutes.
Nakamura's cross to the back post was headed across the face of goal by Vennegoor of Hesselink and Riordan fired home.
Japan midfielder Nakamura almost made it two with a fine, curling free-kick tipped wide by goalkeeper Graeme Smith.
Boruc did well to block from Darren Smith after the Motherwell midfielder broke clear.
McGeady was just wide at the other end with a curling effort from the edge of the box.
Celtic: Boruc, Caldwell, Pressley, O'Dea, Naylor, Nakamura, Lennon, Hartley, McGeady, Zurawski (Riordan 35), Vennegoor of Hesselink (Beattie 83).
Subs Not Used: Brown, Miller, Gravesen, Perrier Doumbe, Bjarnason.
Booked: Naylor.
Goal: Riordan 52.
Motherwell: Graeme Smith, Corrigan, Craigan, Reynolds, Danny Murphy, McBride, Kerr, McGarry, Vadocz, Darren Smith (Jamie Murphy 79), Clarkson.
Subs Not Used: Meldrum, Kinniburgh, Molloy, Quinn, Fitzpatrick, Connolly.
Booked: Craigan, Kerr.
Att: 58,654
Ref: E Smith