Exeter Chiefs earned a home semi-final with four games to spare, while Saracens scored a late try to hurt Newcastle's survival hopes.
Saracens scored a last-gasp try to deny bottom club Newcastle Falcons a losing bonus point at Allianz Park on Saturday.
Alex Lozowski latched onto Owen Farrell's kick in the final minute as Sarries triumphed 26-12 in a hard-fought Premiership encounter.
Sean Maitland finished off a brilliant team move to score the game's first try in the 34th minute, with Max Malins and Nick Tompkins crossing before Lozowski touched down in the closing stages to secure a welcome bonus and deny the Falcons.
Saracens' success at home sees them keep pace with Exeter Chiefs, who ensured home advantage in their semi-final play-off after running in seven tries in a comprehensive 52-20 win over Leicester Tigers at Welford Road.
Henry Slade ran in the pick of four first-half scores after tremendous offloads from Don Armand and Olly Woodburn and he turned provider after the restart when he tore through the Leicester defence and released Ollie Devoto.
Tom Youngs was shown a red card following an illegal clear out after Santiago Cordero touched down and Jack Nowell completed the scoring on a miserable day for the struggling Tigers.
Nathan Hughes grabbed a double as Wasps edged away from the relegation battle by beating second-bottom Worcester Warriors 28-16.
Marcus Watson and Zurabi Zhvania added to Hughes' opener inside the first 15 minutes, with the Warriors - who remain three points clear of Newcastle - unable to build on Sam Lewis' response before the break.
Bath claimed the bragging rights with a 26-19 bonus-point victory over West Country rivals Bristol Bears at Twickenham.