Five penalties from fly-half Ross Broadfoot helped Jersey leapfrog Rosslyn Park to go top of National One.
Full-back Glenn Bryce got Jersey's only try in front of an encouraging 3,600 crowd at St Peter.
Jersey's 20-18 win puts them a point clear of Fylde, with Park dropping to third, but only two points off the top.
"Ross Broadfoot was cool under pressure. He's used to playing in front of big crowds," director of rugby Ben Harvey told BBC Jersey Sport.
"If you want to hang your hat on someone to knock your goals over, he's your man. He did that brilliantly today."
The visitors went ahead early on when Steve Parsons went over, but Broadfoot reduced the arrears with his first penalty.
Eight minutes from the break, an interception by Jersey back-row forward Guy Thompson deep in his own half eventually found its way to Bryce for Jersey's sole try, which gave them an 8-5 advantage at the break.
Broadfoot then kicked four more penalties, Park's Ross Laidlaw responding with two of his own before Graham Barr made the scoreline a little closer with a converted last-minute try.