Ospreys were no match for Saracens on Saturday, while Exeter Chiefs were among the other European Champions Cup winners.
After one appearance at the Rugby World Cup, England international Joe Cokanasiga appears set for a lengthy spell on the sidelines.
Ireland centre Garry Ringrose was the star of the show as Leinster started their bid to regain the Champions Cup with a bonus-point win.
A looming points deduction would see Saracens facing a Premiership relegation battle this season, but they defeated Gloucester on Saturday.
Saracens were on the brink of a second defeat in three Premiership games but they battled back to defeat London Irish.
Exeter Chiefs fell to a narrow Premiership defeat at Bath, as Stuart Hogg's first appearance ended in disappointment.
Nathan Hughes made a big impact on his Premiership debut for Bristol Bears, while Luke Morahan claimed a brace in an emphatic derby win.
Munster, Racing 92 and the Ospreys will take on holders Saracens in the pool stage of the 2019-20 European Champions Cup.
Northampton Saints took the final Premiership play-off spot despite losing to Exeter, while Bath secured Champions Cup rugby next term.
Although their chances of reaching the play-offs were remote, Wasps still had hope until slumping in the second half at Bath on Sunday.