Bath finished the game with 11 men as they suffered defeat to lowly Worcester Warriors in the 98th minute.
Bristol Bears ended 2018 with a huge win over Newcastle Falcons, while Bath moved up to fifth with victory over Leicester Tigers.
Saracens had not suffered defeat since April, but they were soundly beaten by Exeter Chiefs to lose top spot in the Premiership.
La Rochelle's perfect record in the Challenge Cup was ended by Bristol, but Clermont Auvergne claimed a fourth win out of four.
Defending champions Saracens have won each of their opening nine Premiership fixtures as they stayed perfect by beating Wasps 29-6.
There were wins in the Premiership on Saturday for Exeter, Sale and Wasps, the latter triumphing despite a stunning Bristol fightback.
Bristol led Exeter by 14 points in the second half, but Rob Baxter's side snatched a dramatic victory in time added on.
Connacht had no answer to Chris Ashton, who enjoyed a hat-trick on his competitive debut for Sale Sharks.
Worcester Warriors had lost 11 away games in a row in the Challenge Cup, but ended that sequence with a brilliant showing in Paris.
Prop Ryan Bower saw red but Worcester Warriors still ran in seven tries to record their first home win in the Premiership this season.