Gloucester came from Ashton Gate with a bonus-point victory after seeing off Bristol with a 32-14 victory on Friday.
Bristol desperately needed to win in order to close the gap on 11th-placed Worcester Warriors, who remain seven points clear.
Billy Burns opened the scoring in the third minute for the Cherry and Whites with a penalty, countered by new Bristol fly-half Billy Searle to make it 3-3.
Gloucester then went ahead again with the game's first try thanks to Charlie Sharples, the former England wing breaking tackles down the touchline before having the speed to finish in the corner.
Burns impressively converted from out wide and a second penalty stretched the lead to 13-3, before full-back Tom Marshall was sin-binned for a deliberate knock-on. Searle converted the resulting three-pointer to leave Gloucester ahead 13-6 at half-time.
Searle's third penalty helped Bristol move within a converted try before Gloucester produced an unusual score, England wing Jonny May controlling a sliding ball with his legs after a spill from Luke Arscott before offloading to Burns for the try.
Lewis Ludlow was the next over for Gloucester to give the visitors' some breathing room, but Max Crumpton's try off the bench for Bristol gave the Premiership's bottom side hope of snatching a losing bonus point.
But despite Bristol's late attacks it was Gloucester who had the final say, May speeding clear to secure the bonus-point win for the Cherry and Whites.
Pens: Searle 3
Tries: Sharples, Burns, Ludlow, May
Cons: Burns 3
Pens: Burns 2
Yellow Card: Marshall
Bristol: 15 Jason Woodward, 14 Jack Wallace, 13 Will Hurrell, 12 Tusi Pisi, 11 David Lemi, 10 Billy Searle, 9 Alby Mathewson, 8 Mitch Eadie, 7 Jack Lam, 6 Sam Jeffries, 5 Mark Sorenson, 4 James Phillips, 3 Gaston Cortes, 2 Marc Jones (c), 1 Ryan Bevington
Replacements: 16 Max Crumpton, 17 Jack O’Connell, 18 Jamal Ford-Robinson, 19 Jordan Crane, 20 Nick Fenton-Wells, 21 Rhodri Williams, 22 Jack Tovey, 23 Luke Arscott
Gloucester: 15 Tom Marshall, 14 Jonny May, 13 Henry Trinder, 12 Andy Symons, 11 David Halaifonua, 10 Billy Burns, 9 Willi Heinz (c), 8 Ben Morgan, 7 Jacob Rowan, 6 Sione Kalamafoni, 5 Jeremy Thrush, 4 Tom Savage, 3 Josh Hohneck, 2 Richard Hibbard, 1 Paddy McAllister
Replacements: 16 Motu Matu’u, 17 Yann Thomas, 18 Paul Doran-Jones, 19 Tom Denton, 20 Lewis Ludlow, 21 Callum Braley, 22 Billy Twelvetrees, 23 Charlie Sharples
Referee: JP Doyle
Assistant Referees: Jack Makepeace, Ross Campbell
TMO: Rowan Kitt