It was a lively start from both sides in front of a large crowd in the sun at Windsor Park.
Glentoran created the better chances in the first half, with Jordan Stewart squandering three good opportunities in quick succession.
His first arrived on 10 minutes when Danny Amos played in a low corner from the right which former Linfield midfielder Stewart met, but he hooked an effort over the crossbar.
Two minutes later Ben Hall’s clearance ricocheted off Stewart and fell invitingly for the 30-year-old, but he snatched at the chance and blazed over from inside the box.
He came closest to breaking the deadlock on 15 minutes when Josh Daniels’ cross fell for Stewart on the opposite side and his low first-time effort fizzed just wide of the far post.
Daniels then had a shot blocked before Kirk Millar flashed a half-volley wide at the other end for the Blues.
After a lull in the game, Stewart had another big chance before the break.
Patrick Hoban’s shot was deflected into path of Stewart, but just as he went to shoot, Isaac Baird nipped in to turn the ball behind.
Linfield had the first meaningful chance of the second half on 54 minutes as Kyle McClean produced a clever flick into the path of Matthew Fitzpatrick, whose drilled effort was tipped over by Billy Crellin.
Soon after, at the other end, Amos’ half-volley was pushed behind by Chris Johns.
There was then a VAR intervention on 84 minutes for a brief check for a handball in the Linfield box that was quickly cleared.
The game fizzled out and extra time was required, which was equally as cagey as the end to normal time.
That was until four minutes from the end when late drama ensued as the ball was zipped into McKee, with Kamson-Kamara diving in to bring down the Blues substitute.
He kept his composure to send Crellin the wrong way and snatch a late win for Linfield as they secure a third success in this competition in four years.
