Guernsey manager Ian Champion said: "It was amazing really, not only the first win for some time but my first win as coach as well."
Jersey keeper Helen Lagadu had no chance of stopping Rochelle Vaudin's 30 yard shot.
"It was a cracking advert for ladies football. It was very close, but I'm just delighted it went our way."
Jersey enjoyed more territory in the first half, hitting the bar with a Louise van de Vliet header, but that was the closest they came to a goal.
Jersey lacked the extra penetration and creativity needed to produce an equaliser and when they did reach the Guernsey penalty area, centre back Vicki Rang was a rock.
This was the first Muratti win for Guernsey in seven years
Guernsey's Natalie Granger had the best chance to score in the second half, but her tame shot was easily collected by Lagadu in the Jersey goal.
Jersey manager Tony Hoyland said: "We've come into this on the back of one game and maybe that's the difference - just getting the games under our belt.
"But, from a development point of view it was a good step forward for us. It's a disappointing result and everyone is gutted but it's a good step forward."
It was better news for Jersey's Under-16s who beat Guernsey 6-2 in the first Girls Muratti.
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