Motherwell’s Cedric Kipre was sent off in the 41st minute after kicking out at Celtic captain Scott Brown, who had pushed the defender after the pair had tumbled to the floor.
The 21-year-old Frenchman was also sent off by referee Craig Thomson for conceding a penalty in Celtic’s Scottish League Cup final win at Hampden Park in November.
Despite their numerical advantage, Celtic left Fir Park frustrated after failing to make the breakthrough.
Celtic moved 10 points clear of Rangers with a game in hand and remain on course for their seventh successive Scottish Premiership title.
Celtic’s on-loan goalkeeper Scott Bain, who made his debut in the Old Firm win over Rangers last week, kept his place at the expense of fit-again Dorus de Vries and was the busier keeper in the first half.
Motherwell midfielder Chris Cadden fired a decent long-distance drive at Bain, who moments later made a more impressive save from a close-range Curtis Main header.
Bain was called into action again to keep out Ryan Bowman’s powerful volley from just inside the box, before flying to his right to fist Main’s ferocious 30-yard free-kick wide for a corner.
Four minutes before half-time, Kipre got his marching orders for reacting to Brown’s push.
Motherwell goalkeeper Trevor Carson made saves from James Forrest and Tom Rogic as the champions stepped up the pace early in the second half.
Celtic boss Brendan Rodgers sent on Scott Sinclair, Stuart Armstrong and Patrick Roberts as the league leaders pushed for a winner.
Roberts skimmed the bar in the 81st minute with a left-footed drive and Armstrong came close with a curling shot from the edge of the box.
Motherwell defender Richard Tait blocked a Sinclair shot as Celtic were kept at bay in a tense finale.
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