But having bossed the first-half, they lost the second 29-10. They took their try count to six, matching the number they scored in six Pool matches in their debut season in the tournament in 2012/13, but conceded four to give the Blues something to take away with them after a harrowing afternoon in the west country that ended in a 44-29 defeat.
The Chiefs travel to Glasgow Warriors on Sunday to meet a team who beat them in a pre-season friendly at home in August. The Scotstoun clash will be vital if they are to stay in the hunt for a quarter-final spot in a Pool that also contains the reigning champions Toulon.
The French side also picked up a bonus point after 32 frantic minutes at Stade Mayol against the Warriors. They led 34-0 at half-time, yet like the Chiefs lost the second half 28-17.
Like the Blues, the Warriors got up off the canvas to hit back and they ran in four tries, two by Canadian wing DTH van der Merwe, to at least take a point away with them against a team that had only conceded six tries in nine games in the Top 14 to date this season.
While the Warriors get ready for a home clash in round two, Toulon head to Cardiff to face the Blues at the Arms Park. They had Springbok wing Bryan Habana watching from the sidelines in round one. Will he make his club debut at the Arms Park on Saturday?