The Steelmen competed very well in the first half but never recovered from conceding the goal in first half stoppage time, with the title challenging Hoops dominating the second period without adding to their tally.
Motherwell survived a major scare inside the first four minutes when James Forrest should have scored when sent clean through on Liam Kelly but the away keeper blocked his effort.
Jake Carroll – playing in the unfamiliar position of centre back beside Bevis Mugabi for ’Well due to an injury crisis – then slid in to make a crucial block from a Rogic shot.
It was then the Steelmen’s turn to be unlucky when Callum Slattery sent in a lovely curling shot which had home keeper Joe Hart beaten but hit the crossbar.
Forrest had to go off injured and was replaced by Mikey Johnston, before visiting striker Kevin van Veen was booked for deciding to step in as Hart took a goal kick. Van Veen got a boot from the keeper into the bargain.
’Well came so close to breaking the deadlock when Hart made a fantastic save from a deflected shot by Sean Goss, before reacting superbly to stop the rebound from Tony Watt but Watt was adjudged to be offside.
Kelly was called upon to make a wonderful save from ex-’Well star David Turnbull, but Celtic scored on the brink of half-time when Turnbull squared a free-kick to Rogic who shot in with his left foot.
Australian star Rogic nearly made it 2-0 early in the second half but his attempt was blocked by Kelly’s leg. Liel Abada then headed against the bar for Celtic but he was offside.
Just after the hour mark, Rogic scooped an effort well over after a Nir Bitton pass.
Kelly then saved a Johnston header as Celtic dominated the second period.
Although ’Well then forced a couple of corners, nothing came of them and Celtic produced another attack which culminated in Rogic fluffing his lines.
Abada sent a shot a couple of feet wide after 87 minutes in the last chance of the game.
Motherwell, fifth in the Scottish Premiership with 25 points from 18 games, continue their league campaign in a home game against St Johnstone on Saturday.
Celtic: Hart, Juranovic, Carter-Vickers, Starfelt, Taylor, Rogic, Bitton, McGregor, Abada, Turnbull, Forrest (Johnston 18) (Ralston 77).
Motherwell: Kelly, O'Donnell, Mugabi, Carroll, McGinley, Slattery (Donnelly 72), Maguire, Goss, Woolery (Roberts 86), van Veen (Shields 72), Watt.
Referee: Euan Anderson