Two first-half tries from winger Tom Varndell set the platform for promotion-hopefuls Bristol to overcome Jersey at St Peter.
Varndell's first score, in the corner after just one minute, gave the islanders an uphill task and they trailed 17-0 at the break.
Tom Howe sprinted in for Jersey's only try after good work from Gary Graham.
Flanker Olly Robinson crashed over from a maul at the other end to put the result beyond any doubt.
Jersey: Lane, Howe, Evans, Robling, McCrea, Cope, Moates; Lancuba, Garcia-Veiga, Garfagnoli, Markham, Campbell, Rae (capt), Graham, Haining.
Replacements: Selway, McCarthy, Herriott, Butterworth, Dudley, Adair, Cooke
Bristol: Wallace, Varndell, Tovey, Carpenter, Edwards, Henson, Cliff; Genge, McMillan, Cortes, Glynn, Sorenson, Koster, Robinson, Eadie.
Replacements: Jones, Traynor, Ford-Robinson, Townson, Phillips, Hampson, Jarvis.