Brett Connon held his nerve with a late penalty to give Newcastle victory at Wasps, while Exeter also did the Falcons a favour.
Saracens eased past Northampton Saints but table-topping Exeter Chiefs had to repel a second-half rally from Sale Sharks.
Saracens' defeat on Friday left the door ajar for Exeter Chiefs, who downed Newcastle Falcons to go top of the Premiership.
Leaders Exeter Chiefs suffered a third Premiership defeat of the season at Gloucester, while Wasps moved into the top four.
Jack Nowell, Henry Slade and Luke Cowan-Dickie have all signed fresh two-year deals with Exeter Chiefs, it has been announced.
Saracens and Racing 92 secured home quarter-finals in the Champions Cup but the hopes of Exeter Chiefs are over after defeat at Munster.
Premiership champions Saracens are through to the last eight of the European Champions Cup after beating Lyon on Sunday.
Bath finished the game with 11 men as they suffered defeat to lowly Worcester Warriors in the 98th minute.
Having suffered their first Premiership defeat of the season in their last away game, the Exeter Chiefs lost again at Northampton Saints.
Saracens had not suffered defeat since April, but they were soundly beaten by Exeter Chiefs to lose top spot in the Premiership.
Ulster and Exeter Chiefs enhanced their chances of qualifying for quarter-finals of tEurope's premier club rugby competition on Friday.
There were wins for Gloucester, Toulon and Leinster in the European Champions Cup on Saturday.
Harlequins won an entertaining encounter with Exeter Chiefs to hand them their first defeat of the Premiership season.
Jack Nowell left the England camp with an injury last week and Exeter Chiefs have confirmed he suffered a torn hamstring.
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.