Bath: (6) 12
Pens: Barkley (4)
Bristol: (6) 19
Tries: Robinson
Con: Hill
Pens: Hill (4)
Bristol beat neighbours Bath to consolidate their position behind leaders Gloucester in the Premiership.
It was a fourth successive defeat for Bath, despite Danny Grewcock and Olly Barkley returning for them after England duty and injury respectively.
Two penalties apiece from David Hill and Barkley made it 6-6 at half-time.
Hill and Barkley added a penalty each before Hill put Lee Robinson in for a try which he converted. Bristol held out despite a fourth Barkley penalty.
Bath's acting head coach Steve Meehan:
"I can't question the effort. We put them under so much pressure. We're trying to attack, trying to play rugby. "There's too much talent here and players are working too hard to be denied. It's just a question of sticking at it.
"I can't feel anything but pride for the effort."
Bristol's director of rugby Richard Hill:
"I'll have to keep the boys off the cider. It'll be top two in the league. Gloucester are on fire and we're not too bad either. "It's my first win here at Bath as a coach. It means a lot to me and I am pleased - I can even walk home because I still live in Bath.
"We knew it wasn't going to be a classic. But I'm pleased."
Bath Perry; Maddock, Barkley, Fuimaono-Sapolu, Abendanon; Berne, Walshe; Barnes, Hawkins, Flatman, Short, Grewcock, Beattie (capt), Scaysbrook, Faamatuainu.
Replacements: Ward, Ovens, Louw, Goodman, Travagli, Walker, Bory.
Bristol: Arscott; Robinson, Brew, Higgitt, Morgan; Hill, O'Riordan; Hilton, Regan, Crompton, Winters, Llewellyn (capt), Budgett, El Abd, Ward-Smith.
Replacements: Blaney, Clarke, Lewis, To'oala, Nicholls, Strange, Cox.