- Alfredo Morelos (64')
- Kyogo Furuhashi (44', 56')
Celtic dominated throughout the contest to claim a third trophy under manager Ange Postecoglou.
Furuhashi, who also scored twice in a 2-1 win over Hibernian in last season's final, missed a gilt-edged opportunity to put Celtic ahead in the 42nd minute, sending a header over the bar.
Yet he quickly made amends by drifting into the six-yard box and slotting home a Greg Taylor cross two minutes later.
Michael Beale's side pulled one back in the 64th when James Tavernier delivered a cross from a free kick that was turned in by Alfredo Morelos, but despite late pressure they could not find an equaliser.
"It means the world to me. Time after time, you're tasked to win at this club," Celtic captain Callum McGregor told the BBC. "This is a special group. We can do both sides of the game. Listen to this place. It's rocking."
The game was marred by a clash between fans ahead of kick off. A Police Scotland spokesperson said "enquiries are ongoing following a disturbance involving a large group outside Hampden Park..."
The teams will now shift focus back to the Scottish Premiership, where Celtic are top of the standings with 73 points from 26 games, while second-placed Rangers are nine points behind them on 64.
- Nick Walsh