Bristol went ahead when David Lemi found fellow winger Tom Arscott, who stepped inside Brown to touch down.
After a scoreless first half, Samoan wing David Lemi made the breakthrough with a try on the resumption.
David Lemi's converted try then gave Wasps a 17-10 lead at the break.
Bristol should have scored when replacement Andrew Blowers knocked-on over the line before wing Lemi grabbed a late consolation.
Neil Brew and David Lemi tries earned Bristol a bonus point but they slipped to a third straight league defeat.
Steve Kefu sent in David Lemi after the break, while the Dragons lost Nigel Hall, Phil Price and Tovey to injury.
Wasps regular David Lemi fills the right wing slot for Samoa while Tasesa Lavea of Clermont will direct operations at fly-half.
Bristol might have scored on the resumption when Shaun Perry broke away but his chip ahead for Lemi was too long.
Bristol started brightly, with only an unfortunately timed knock-on by David Lemi preventing them claiming the opening try after 15 minutes.
First, Ben Broster drove across the line then, after the break, David Lemi went over to put Wasps 15 points ahead.
Yet they took the lead for the first time on 46 minutes as Kefu's break sent Lemi in for an unconverted try.
Then, within five minutes of the restart, centre Steve Kefu and full-back Mark van Gisbergen combined well to send Lemi over the line.
Alex Brown and Lamb scored further tries and although David Lemi grabbed a late consolation, Gloucester are up to their highest position all season.
But Samoa still field a backline that has Seilala Mapusua, another Exile, David Lemi of Wasps, Anitelea Tuilagi of Sale and Clermont's Gavin Williams.
Two late tries by David Lemi were little consolation for the visitors who drop to second and need to recover before Wednesday's West Country derby against Bath.
Bristol, who could only get six points on the board in reply, improved after the break and David Lemi's try on 44 minutes gave the visitors hope.
Toulouse looked set for a home quarter-final until a last-minute try from Wasps wing David Lemi saw them beaten in High Wycombe in Sunday's final round of pool fixtures.
Wasps looked shell-shocked and things went from bad to worse when scrum-half Joe Simpson, who had a lively game, dropped a try-scoring pass from David Lemi five metres from the line.
The visitors had scrum-half Danny Care yellow-carded for persistent infringement just before the break and Bristol took advantage when wing Anthony Elliott linked up with Rob Higgitt to put Lemi clear to score in the corner.
Lemi exploded through a crowd of defenders to score a converted try as Bristol enjoyed the better of the closing stages but it was little consolation for the visitors as Gloucester secured the West country bragging rights.
Bristol, who are now also safe from relegation after London Irish's win over Leeds, looked down and out but they began the second half strongly and after Bath made a hash of an attacking scrum, Lemi was able to touch down.
It was a sad way for Bristol to bow out of the league and for their veteran hooker Mark Regan to call time on his career, while scrum-half Shaun Perry, winger David Lemi and number eight Dan Ward-Smith were also playing their last games for the club.
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