In Pool Four Biarritz and Saracens look a class above Glasgow and Italian minnows Viadana.
And David Tait went over in the corner as Sale finished second in Pool One.
Ireland will take on Australia, Italy and the second qualifiers from Europe and the Americas in Pool C.
Wales are in the Plate after finishing third in Pool B to drop out of the first-tier Cup competition.
South Africa are in Pool A along with Wales, Australia and New Zealand.
The Tigers are currently four points ahead of the Ospreys in Pool Three.
Connacht maintained their hopes of catching London Irish in Pool One with a 30-3 win over Rovigo on Friday.
The other two teams in Pool C, Venezuela and the Dominican Republic, are among the most fearsome in the tournament.
Tournament favourites New Zealand are in Pool A alongside France, Tonga and the top qualifiers from the Americas and Asia.
In Pool D, Wales face holders South Africa, their 2007 conquerors Fiji and the top teams from Oceania and Africa.
With both teams' chances of qualifying for the quarter-finals already extinguished, only a second-placed finish in Pool Four was at stake.
Wales line up against New Zealand, Australia and South Africa in pool A, while Scotland face France, Canada and Sweden in pool C.
The victory puts Bristol ahead of Stade Francais in pool three and level on points with Cardiff with just two games to go.
The three-time European champions eased seven points clear in Pool 5 - closest challengers Bath visit Glasgow on Sunday - after subduing the spirited hosts.
Munster, who had picked up a bonus point from their opening 24-23 defeat by Wasps, climb above Clermont to take second spot in Pool Five.
The U.S. will play in Pool C with two-time champions Australia, Ireland, Italy and another European team, while Uruguay can still qualify through further playoffs.
Bristol's reward for finishing third in the Premiership last season is to be drawn in Pool Three against French champions Stade Francais, Cardiff and Harlequins.
The Blues finished second in Pool One of the Heineken Cup behind all-conquering Northampton Saints who romped through to the knock-out stages with a 100% record.
They have been drawn against last year's cup runners-up Bourgoin from France, Italian side Overmach Parma and Romanian Champions Bucuresti Oaks in Pool One of the competition.
The defeat to South Africa left England third in Pool A, needing to win their two remaining games against Samoa (22 September) and Tonga (28 September) to progress.
The result cemented second place for Gloucester in Pool Six behind the unbeaten Cardiff Blues with two games remaining, the next being at home to the Blues in January.
After an opening bonus-point win at Edinburgh, this victory puts the Irish province in pole position in Pool Two, with home and away fixtures against Castres next up in December.
In Sunday's late match, South Africa ran in nine tries to dispatch the United States 64-15 to round off their perfect winning record in Pool A which they topped from England.
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Wales face India, Tonga and South Africa in Pool A and if they progress to the quarter-finals will face the winners or runners-up from Pool B - New Zealand, Scotland, Canada or Guyana.
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But Munster's 28-14 triumph against the Exiles means the Ospreys finished a disappointing third in Pool Three - therefore missing out on the consolation prize of qualification for the second-tier Amlin Challenge Cup.
They currently lie in third place in Pool Four on 13 points but can still mathematically qualify for the knock-out stages if they get a bonus-point win at Biarritz and Aironi beat Ulster at home.
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Winning a Heineken Cup match away from home is something Edinburgh, who also face Guinness Premiership champions Wasps in Pool 2, have not managed since 2004, the only time they got beyond the pool stages.
The last two winners are in Pool Five with Wasps and 2006 champions Munster joined by the Scarlets, who reached the last four last season, and Clermont, who have just finished runners-up in the French championship.
France are engaged in a three-way fight with Argentina and Ireland for the two quarter-final places in Pool D and they had no margin for error after their 17-12 defeat by the Pumas which opened the tournament.
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