The Bears’ bonus-point win, which saw them overtake local rivals Bath in the standings, was rarely in doubt as they scored five tries against an Irish who could not follow up their heroics in winning at Exeter last time out.
Semi Radradra, Ben Earl, Harry Thacker and Will Capon crossed for the visitors, who were also awarded a penalty try. Max Malins added the rest of Bristol’s points with a penalty and three conversions.
Irish could only respond with a second-half try from Ollie Hassell-Collins which Paddy Jackson converted.
Following a scrappy opening to the game, Bristol took the lead in the 13th minute with a splendid try.
Near to his own 22, Piers O’ Conor fielded a speculative kick before setting off on a superb 50-metre run with Radradra up in support to receive the scoring pass.
That converted try was the only score of the opening quarter but Bears became increasingly dominant, bossing the game in terms of possession and territory.
Inaccuracies in passing and ball retention prevented them from initially capitalising but it came as no surprise when the visitors extended their lead on the half-hour.
After turning down a number of kickable penalties in favour of attacking line-outs they were rewarded when Earl crashed over from one of them.
Irish were now firmly under the cosh and should have conceded a third try but Malins, when under no pressure, inexplicably let the ball fall from his grasp as he went to touchdown.
However, the fly-half was able to partially atone for that error by kicking a straightforward penalty to leave Bristol with a 17-0 lead at the end of a one-sided first half.
After the restart, Irish built up their first piece of sustained pressure but it came to nothing as they conceded a penalty for not releasing which enabled Bristol to clear their lines.
Despite that, the home side continued to have the better of ultimately a scoreless third quarter with Bristol becoming complacent in the miserable conditions.
They paid the penalty as Irish got on the scoreboard just after the hour with an excellent solo try from Hassell-Collins, who evaded a number of defenders on a 45-metre run to the line.
Bristol brought on Callum Sheedy and Kyle Sinckler to raise them from their slumbers and it soon paid dividends.
First Thacker finished off a driving line-out before referee Karl Dickson awarded a penalty try for collapsing another drive to give Bears their bonus point target with four minutes remaining.
With the last move of the match, another line-out drive saw Capon score Bristol’s fifth before they celebrated as news came through of Bath’s failure to win and ensure their qualification.
