Jersey battled back into the game but were ultimately not able to recover from two tries by former England wing Tom Varndell.
The clock had only just ticked past 60 seconds when Varndell crossed in the corner after impressive approach work from fellow winger Ryan Edwards, a late addition to the visiting XV in place of Charlie Amesbury. Gavin Henson converted and soon added a penalty goal to his side's tally.
Bristol continued to have the better of the battle for territory and possession, benefitting from a brisk easterly breeze at their backs, and Varndell added a second when the ball was fed to the right and Henson supplied the scoring pass.
Jersey had little to shout about in the first half but were more prominent after the break when an impressive charge by Nick Haining could have set up Tom Howe, but the wing just lost his balance as he sought to accelerate clear. There was no stopping Howe at the second time of asking however when Gary Graham broke through and supplied the scoring pass.
Jersey's forwards had struggled at scrum time early in the game, but gradually achieved parity. One second-half attempt to score via a catch-and-drive was unsuccessful after the maul rolled around 30 metres sideways, but not forwards, with Bristol able to neuter the threat without incurring the referee's wrath.
Jersey went down to 14 players for the final five minutes after losing lock Nick Campbell with a suspected broken ankle, and Bristol capitalised with an attacking lineout, where possession was secured and Olly Robinson drove over.
"It was a frustrating day and I think we were caught like a rabbit in headlights at the start and showed Bristol a bit too much respect," said Jersey Head Coach Harvey Biljon. "We needed to keep the ball and not give up territory, but we did the opposite.
"I was pleased that we came back into the game and I don't think you can question the character and desire of the squad.
"I said before the season started that I was going to have some selection headaches, but unfortunately that's not the way things are operating at the moment with the number of injuries that we have."
Bristol's defensive effort pleased Director of Rugby Andy Robinson.
"I'd challenged the boys to concede fewer than 20 points, so it was a great defensive effort," he said. "Scoring two well-executed tries early on was a really good start, but we had to work hard after that against a good Jersey side - this is a tough place to come."
JERSEY: Lane, Howe, Evans (Cooke 52), Robling, McCrea (Adair 54), Cope, Moates (Dudley 54); Lancuba (McCarthy 66), Garcia-Veiga (Selway 66), Garfagnoli (Herriott 32), Campbell, Markham, Rae (c) (Butterworth 58), Graham, Haining
BRISTOL: Wallace, Varndell, Tovey, Carpenter (Townson 77), Amesbury, Henson (Jarvis 58), Cliff (Hampson 58); Genge (Traynor 52), McMillan (Jones 52), Cortes (Ford-Robinson 38), Glynn, Sorenson, Koster (Phillips 64), Robinson, Eadie.
Referee: Luke Pearce (RFU)
Star man: Tom Varndell (Bristol)
Half Time: 0-17
Tries: Howe 65
Conversion: Cope 65
Tries: Varndell 2, 26, Robinson 77
Conversions: Henson 2, 26, Jarvis 77
Penalty: Henson 8
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