Pitched in against a rough-house set of forwards who were physically prepared to drive the ball and a backline capable of stringing extensive phases of play together, Bayonne looked a considerably better side than the one at the start of the competition.
But Gloucester did particularly well in the scrum and dominated that area throughout. And when they maintained the tempo and momentum of their rugby in the right parts of the field, looked a dangerous side.
Through the concerted efforts of Jake Boer, who is playing some mean and moody rugby just now, Peter Buxton, the heavy duty back rower and Marcel Garvey, who had an outstanding game defensively, Gloucester had enough in most areas of the field.
They took the lead after nine minutes with a lovely try. A line-out was carried forward by Peter Richards and Ludovic Mercier before Luke Narraway added his weight to the attack and Adam Eustace thundered through a big game in midfield.
And when possession came back, prop Gary Powell burst over for the first of his two tries.
But Gloucester's control did not last. Mercier was penalised for a high tackle and Bayonne kicked the penalty to the corner. Steve Hall claimed the line-out and the visiting forwards pushed Gloucester over with some comfort for loosehead prop Aretz Iguiniz to score.
It cut the advantage to 7-5 and that's how it would stay until the 28th minute when Gloucester scored again.
Bayonne last Richard Dourthe to the sinbin for a late tackle on Mercier and after Gloucester churned their way down field, Alex Brown claimed the line-out and from the drive, Powell was bundled over for his second try.
However, Gloucester required far more tempo to their game to truly put it out of reach and it came two minutes after the break.
Mefin Davies, Richards and Mercier sustained a move to the right but it was Boer's superb surge into the heart of Bayonne's defence that created room for Morgan to power home in the wing position.
Mercier's conversion made it 25-5 and Gloucester were within sight of a bonus point. Again Richards and Mercier were heavily involved and Mike Tindall dropped his shoulder to score to the right of the sticks.
It took Gloucester 32-5 ahead, home and hosed. However, Bayonne suddenly found their feet in the last quarter and scored two tries.
Gloucester lost Tindall to the sinbin for killing the ball and with five minutes to go replacement Christophe Laurent scored from close range following a series of powerful surges and good ball retention.
And it was to Bayonne's credit that they were able to score again in stoppage time. Despite some outstanding defence from Garvey, Benjamin Thierry found his way home down the left.
Dourthe's conversion made the score 35-19 and far closer than it should have been - but Gloucester secured a home tie in the last eight.