Irish booked a European Challenge Cup semi-final with Newcastle after running in seven tries against the French side.
London Irish (10) 48
Tries: Russell 2, Pedro Tiesi, Flutey, Ojo,
Cons: Flutey 4, Geraghty
Bayonne 5 (0) 5
Try: van Shalkwyk
A big forward push led to Robbie Russell scoring the first try, but though the Exiles dominated they could not find the points in the first half.
But Russell surged over and Topsy Ojo touched down to complete a superb move involving influential Olivier Magne.
Replacement Phil Murphy was soon on the scoresheet and Bob Casey completed the tries when he dived between the posts.
London Irish boss Brian Smith:
"At 10-0 at half-time, I thought we were massively ahead of them because we played all the rugby in the first-half but, for whatever reason, we failed to get across the line a couple of times.
"The good thing was that the chat was very positive at half-time and I think the boys applied themselves very well.
"Once they crumbled, I thought we were ruthless with our execution in the second half and it was an outstanding performance.
"I thought we controlled the game quite well. We knew they were going to be quite destructive up front and we decided to move them around.
"By the last 20 minutes, they ran out of gas which was part of our plan.
"They hit us on a day when we were prepared to play good, positive rugby."
London Irish: Armitage, Ojo, Pedro Tiesi, Catt, Tagicakibau, Flutey, Hodgson, Collins, Russell, Skuse, Casey, Roche, Danaher, Dawson, Magne, Hatley.
Replacements: Geraghty for Catt (53), Bishop for Tagicakibau (26), Edwards for Hodgson (51), Hatley for Collins (2), Strudwick for Roche (53), Murphy for Magne (65), Paice for Hatley (59).
Bayonne: Noutary, Nunez-Poissek, Dourthe, Roque, Lhande, Fraser, Rouet, Coetzee, Heguy, Wessels, Cleda, Tewhata, Combes, Massabeau, Lamour.
Replacements: Sudre for Rouet (65), Bergez for Heguy (53), Garcia for Wessels (47), McLaren for Tewhata (53), van Shalkwyk for Lamour (62).
Not Used: Hill, Vermis.
Ref: Malcolm Changleng (Scotland).