Gary Hooper broke Motherwell's resistance to stretch Celtic's lead over Rangers at the top of the Scottish Premier League to 23 points.
Kelvin Wilson squandered Celtic's best chance of a first half they totally dominated, heading straight at goalkeeper Darren Randolph.
Randolph's saves kept Celtic at bay until the 59th-minute, when Hooper fired home from close range.
Well had one shot on target as their six-game unbeaten run came to an end.
For Celtic, it was a 14th straight win in all competitions and their 17th in the SPL.
Home manager Neil Lennon again rang the changes as he looked to keep his players fresh with the title all but won after reigning champions Rangers were docked 10 points for going into administration.
Adam Matthews, Thomas Rogne, Victor Wanyama, James Forrest and Georgios Samaras came in for Cha Du-ri, Emilio Izaguirre, Kris Commons, Anthony Stokes and captain Scott Brown, who has a groin injury.
Motherwell, looking for their third win in eight days, made only one change, with captain Keith Lasley returning from suspension to replace Omar Daley in midfield as manager Stuart McCall vowed to attack the leaders.
But it was Celtic who started where they left off against Dunfermline in midweek, dominating possession and Tom Hateley, goalkeeper Darren Randolph and Stevie Hammell were all forced into making important early interceptions for the visitors.
Charlie Mulgrew was full of confidence in a week when he followed his inclusion in the Scotland squad by being named Celtic captain for the day.
He loped forward and set up Samaras before firing wide after the striker's own effort rebounded back into the defender's path off Hateley.
The pair combined again moments later and the Greek's shot was cleared at the second attempt by Randolph as the goalkeeper juggled the striker's effort.
Another Hateley block denied Samaras at the back post after Matthew's cross found the head of the striker, whose effort on the rebound was also deflected for a corner.
Motherwell survived the pressure but were finding it impossible to create chances of their own and Ki Sung-Yueng came close with a drive that flew just wide of the visitors' goal.
A Ki free-kick gave Kelvin Wilson a great chance to open the scoring from eight yards, but the defender headed straight at Randolph.
Stokes came on for Wanyama after the break and the change appeared to disrupt Motherwell's concentration as they poorly defended a long throw chested down by Samaras into the path of Hooper, who scored with clinical precision.
Randolph saved well to deny Hooper as he looked for a quickfire double after again being set up by Samaras.
The Motherwell goalkeeper did well again to save from close range after Forrest threatened on the break.
Motherwell's in-form striker, Henrik Ojamaa, at last had a sniff at goal and perhaps would should have done better than fire straight at Fraser Forster as the visitors at last tested the goalkeeper.
Steve Jennings also fired disappointingly wide as Motherwell missed a chance to move level on points with Rangers, who face Inverness Caledonian Thistle on Sunday.