Exeter Chiefs earned a home semi-final with four games to spare, while Saracens scored a late try to hurt Newcastle's survival hopes.
Bristol Bears and Northampton Saints were no match for La Rochelle and Clermont in the European Challenge Cup quarter-finals.
Two tries from Will Skelton helped Premiership title hopefuls Saracens fight back to beat Harlequins 27-20 at London Stadium on Saturday.
Brett Connon held his nerve with a late penalty to give Newcastle victory at Wasps, while Exeter also did the Falcons a favour.
Gloucester let Friday's Premiership match slip through their fingers late on at Bristol Bears.
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.
For the second time in two days, a side racked up a century of points in the Challenge Cup as Bristol Bears routed Enisei 107-19.
Bristol Bears have pulled off a coup by signing Nathan Hughes from Wasps, who are also losing Willie le Roux at the end of the season.
Ryan Mills' last-gasp drop goal put Worcester Warriors into the last eight of the Challenge Cup for the first time in a decade.