Match ends, Motherwell 0, Celtic 2.
Brendan Rodgers became the first Celtic boss since Jock Stein to win four domestic trophies in a row as his side retained the Scottish League Cup.
Motherwell held their own until James Forrest curled an excellent shot into the far corner shortly after the break.
Celtic's Craig Gordon saved superbly from a Louis Moult header.
But 'Well's hopes ended when Cedric Kipre was controversially sent off for a brush with Scott Sinclair, and Moussa Dembele rolled in the penalty.
Motherwell, whose only League Cup triumph came in 1950, looked capable of recording their first win over the Glasgow side in six national cup finals until Forrest struck his third goal in three League Cup final appearances.
And, once Kipre was dismissed and the penalty dispatched, Stephen Robinson's side never looked like preventing last season's Treble-winners clocking up a 65th domestic game without defeat and their 17th victory in their 32nd League Cup final.
For 45 minutes, this final was a battle, a dour struggle full of heavy tackles, misplaced passes, no rhythm and no semblance of anything that might have lifted you off your seat.
Motherwell wanted it that way. They sought to frustrate and stay alive. They hustled and harried Celtic, forcing the Premiership leaders into mistake upon mistake.
It lacked quality and composure but not passion and aggression. In the grind, Kipre was lucky to avoid a card when he went over the top on Dembele.
The striker then responded by going in over the top on Carl McHugh but was not so lucky. He got booked and things carried on; Motherwell concentrating hard and annoying the life out of the favourites.
They got to half-time in good heart. Celtic's go-to men in attack were diminished.
Dembele was unthreatening, Sinclair was hesitant, Stuart Armstrong was nowhere near as involved as you might have expected. Forrest looked dangerous, Callum McGregor had his moments, but they were pretty much on their own.
In Motherwell's manual on how to neutralise Celtic, chapter one was complete, but they never got particularly far into chapter two. Four minutes into the new half, they buckled and Forrest took advantage.
When Charles Dunne and Peter Hartley gave the winger some space to have a pop with his left foot, Forrest was emphatic, his shot curling around the despairing dive of Trevor Carson and into the far corner.
It unlocked the final - with the spirit of the late Motherwell and Celtic midfielder Phil O'Donnell hanging in the air - and it sent Celtic on their merry way.
They had one scare before they kicked for home and had to rely on Gordon making a wondrous reflex save from a Moult header, but as soon as that moment had passed, they went about nailing down their victory.
Dembele should have made it two with a free header that went wide, but the striker would double the advantage within minutes. It was cruel on Motherwell, a decision that infuriated them.
The Frenchman played a lovely ball in behind the Motherwell defence to Sinclair, who fell to the floor. What made him tumble was a gentle hand on his jersey by Kipre, an act Sinclair milked for all it was worth.
The penalty call was bad enough, but when the defender was red-carded on the back of it, Motherwell were sickened and sunk. Dembele went down the middle from the spot - and scored.
The traffic headed just one way after that. Carson saved from Armstrong then beat away a Leigh Griffiths free-kick before having a post get in the way of the latter adding a third goal.
They had more chances. Motherwell hit a post with a terrific Moult free-kick right at the end and that was that.
Celtic basked in the glory of a fourth successive domestic trophy under Rodgers.
It would take a brave - or daft - person to bet against them making it five and six in the months ahead.
One day their run will end. Not even the world's finest fortune-teller could tell you when that day might be though. They remain Scotland's untouchables.
- 21KipreBooked at 58mins
- 6HartleyBooked at 90mins
- 4GrimshawSubstituted forTannerat 51'minutes
- 8McHughBooked at 54mins
- 15RoseSubstituted forFrearat 70'minutes
- 12BowmanSubstituted forCampbellat 64'minutesBooked at 74mins
- 14S Armstrong
- 49ForrestSubstituted forRobertsat 78'minutes
- 42McGregorSubstituted forRogicat 89'minutes
- 10DembeleBooked at 16minsSubstituted forGriffithsat 64'minutes
- 24de Vries
- Craig Thomson
- Shots on Target
Second Half ends, Motherwell 0, Celtic 2.
Louis Moult (Motherwell) hits the right post with a right footed shot from outside the box from a direct free kick.
Scott Brown (Celtic) is shown the yellow card for a bad foul.
Foul by Scott Brown (Celtic).
Louis Moult (Motherwell) wins a free kick in the defensive half.
Attempt saved. Tomas Rogic (Celtic) left footed shot from outside the box is saved in the centre of the goal.
Attempt blocked. Scott Sinclair (Celtic) right footed shot from outside the box is blocked.
Corner, Celtic. Conceded by Charles Dunne.
Substitution, Celtic. Tomas Rogic replaces Callum McGregor.
Attempt missed. Patrick Roberts (Celtic) left footed shot from the right side of the box is too high.
Attempt missed. Leigh Griffiths (Celtic) header from very close range is too high.
Kieran Tierney (Celtic) wins a free kick in the defensive half.
Foul by Craig Tanner (Motherwell).
Corner, Celtic. Conceded by Charles Dunne.
Attempt missed. Callum McGregor (Celtic) right footed shot from outside the box is high and wide to the left.
Foul by Carl McHugh (Motherwell).
Scott Sinclair (Celtic) wins a free kick in the defensive half.
Attempt missed. Scott Sinclair (Celtic) right footed shot from outside the box is too high.
Corner, Celtic. Conceded by Trevor Carson.