Guernsey have won just one of the last seven Muratti finals - beating Jersey on penalties in 2005 - and were forced to overcome the loss of influential captain Matt Warren with a hamstring injury after just 12 minutes.
The first-half was scrappy affair until the Greens gained the edge through Dyer.
The second half proved to be a much more open with both teams creating opportunities, including a disallowed goal for Guernsey.
I think the fans got their money's worth today
Jersey manager Dave Kennedy
Dyer's strike looked to have secured victory, but man-of-the-match Boyle equalised with a cleverly curled shot that whipped into the corner of the net.
No sooner had Jersey equalised than Sarnian Ross Allan was denied a certain goal by Jimmy Styles.
When 30 minutes of extra-time failed to split the teams the Muratti was decided on penalties for the second season in a row.
Jersey manager Dave Kennedy told BBC Radio Jersey: "Before the game both Steve [Ogier] and I said we wanted an eventful game, good entertainment.
"I think certainly the fans got their money's worth today."
Guernsey boss Steve Ogier on his third straight Muratti defeat: "Both sides, I think, could have won it in extra-time.
"But all in all, again the wrong side of a penalty shoot-out for us."
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