The Danes began well in defence of their total when Ben Fitchet was bowled by Toqeer Ahmad for seven early in the second over.
Josh Butler and Tom Nightingale put on 27 runs for the second wicket before the latter was caught for 13 off 12 balls to leave the islanders on 35-2 off 4.4 overs.
New batter Stokes and Butler came together and began to apply the pressure to Denmark’s attack and bring their side above the required run-rate.
The pair played some superb shots to delight the home supporters as they took 26 balls to reach their half-century stand.
They eventually put on 65 runs before Butler was bowled by Saif Ahmad for 43 off 29 balls to leave the islanders on 100-3 midway through the 12th over.
Damarell was trapped lbw by Laegsgaard for two soon after as skipper Ollie Nightingale came out to try and calm any nerves.
Stokes finished with 67 off 44 balls, including a six and six fours, while Nightingale scored 23 not out off 18 balls as the islanders eased to their target with eight balls to spare.
“It means everything,” Stokes told the ICC after the win.
“For those who have been in the team for a while we’ve had 11 years of almost getting there and not quite, but now we’ve finally crossed the line.
“We’re looking forward to playing at a really good standard against some really, really good teams,” he added.
Danish skipper Shah was named player of the tournament having scored 294 runs in five games including scores of 100 and 91.
“I think Guernsey outplayed us today, they played some really smart cricket,” Shah told the ICC.
“They played really well in the powerplay – both with the ball and the bat – so they got the momentum and we were 30 runs short today.
“We have set the standard for the way we want to play in the future and I’m really proud of the guys, reaching the final is amazing.”