The holders started brightly and created a few good opportunities to go ahead with Sean McAllister twice calling Ryan Schofield into action.
He stung the palms of Schofield on three minutes and then forced the goalkeeper to tip an acrobatic effort over the crossbar soon after.
McAllister was involved again two minutes later as he charged down the left and slipped the ball across for Kealan Dillon, who should have done better with his prodded effort from inside the box that was straight at Schofield.
Those early chances for the Swifts sparked Coleraine into life and they threatened for the first time on 11 minutes when the ball broke for Cooper inside the box and his low effort was palmed away by Declan Dunne.
Shevlin then broke the deadlock on 19 minutes, firing home after a defensive mix-up between Dunne and Caolan Marron in attempting to clear a low cross from Lyndon Kane allowed the striker to nip in and score.
The Swifts almost responded immediately as Leo Alves connected with a deep cross from Adam Glenny with a volley that Schofield was at full stretch to turn over before Marron glanced a header onto the base of the post from the resulting corner.
Coleraine doubled their advantage a minute after the restart as Shevlin flicked the ball into the path of Cooper, who fired beyond Dunne from a tight angle.
Rodney McAree’s side responded well to the setback and cut the deficit on 55 minutes as Doyle curled home from the edge of the area after being teed up by McAllister.
They were back in the game for just five minutes as Zane Okoro burst down the left and saw his low shot deflected into the path of Shevlin, who steered home.
The Swifts kept fighting and pulled another goal back on 66 minutes, with substitute Mitchell turning home from inside the area to keep this breathless final on a knife-edge, but Coleraine held on to win a first Irish Cup in eight years.
BBC News
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