Sale boosted their chances of a Premiership play-off place with a bonus-point 31-22 win against Leicester.
Harlequins ran in six tries as they beat Gallagher Premiership table toppers Northampton Saints 41-32 at Twickenham.
Northampton marched to a 40-17 Premiership bonus-point win over 14-man Leicester as they reinforced their status as table toppers on derby day.
It's been eight years since the Premiership had more than three clubs make it to the Champions Cup quarter-finals, but there remain six in play this season.
Northampton showed why they are top of the Gallagher Premiership, beating champions Saracens 41-30, while Leicester held off Newcastle in a dramatic 19-13 victory.
Jarrod Evans' missed conversion with the last kick of the game saw Harlequins edged out 20-19 by Leicester on Friday.
Saracens boss Mark McCall says "everybody would want" Owen Farrell in their side, with Racing 92 believed to be in talks to sign the England captain.
Bath missed the chance to top of the Premiership table as they crashed to a convincing 35-22 defeat to Leicester.
Bath top the Gallagher Premiership at Christmas after winning an absorbing battle with fellow title contenders Harlequins 25-17 at the Rec.
England lock George Martin has agreed a new contract with Leicester Tigers after playing a starring role at this year's Rugby World Cup.
Sale produced a superb second-half show to open their Champions Cup campaign with a 28-5 victory over Stade Francais at AJ Bell Stadium.
A hat-trick of tries from Leicester's Tommy Reffell ensured Newcastle's desperate start to the season continued with a 47-3 Premiership defeat.
Saracens dealt with the early loss of three key players to make it four wins in a row as they rain in six tries during a thumping 38-10 victory over Harlequins.
A round-up of Saturday's Premiership action as Harlequins go top of the table with win at Leicester, while Sale prevail again away to Bristol.
South Africa's World Cup final match-winner Handre Pollard tells Sky Sports clinching the title with the expectancy on the squad made it "extremely special."
Jamie Shillcock returned to haunt former side Bath as he scored the winning penalty with the last kick of the game to snatch Leicester a 25-24 Gallagher Premiership win.
Bath maintained their winning start in the Gallagher Premiership with a 25-16 triumph over defending champions Saracens, while Sale and Bristol were also victorious.
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Players from Northampton and Leicester, including Courtney Lawes and Ben Youngs, will join England's World Cup training squad in Brighton.
Sale reached their first Premiership final for 17 years as they ended Leicester's hopes of back-to-back titles with a 21-13 victory.