Back rower James Forrester was a key man for the Cherry and Whites, with the explosive youngster roaring to a hat-trick of tries within 44 minutes.
He opened the scoring inside five minutes with the first of his three and then repeated the feat four minutes later, before fellow back-row Andy Hazell chipped in with one of his own.
Bristol managed to add to two Felipe Contepomi penalties before England squad wing Phil Christophers grabbed a try on the half hour to bring the home side to within shooting distance of their opponents, but when the second half got under way it was Forrester's third try that effectively ended hopes of a Bristol comeback.
Australian Shane Drahm added a penalty and a late try for the home side, but by then Gloucester fly-half Ludovic Mercier and England 'A' wing Marcel Garvey had put them beyond reach, throwing Bristol back in the relegation mixer while Gloucester continue to sit pretty at the top of the pile.
For Bristol:Tries: Christophers, DrahmCon: ContepomiPens: Contepomi 2, Drahm
For Gloucester:Tries: Forrester 3, Hazell, Mercier, GarveyCons: Mercier 4