Saracens were made to sweat by Treviso before they eventually overcome the Italian outfit 26-20 to secure their place in the last eight.
Needing just a point to safeguard their passage through to the knockout stages, the English heavyweights laboured and had to erase a 17-13 half-time deficit before pulling clear in the second half.
Mouritz Botha and David Strettle both touched down for Sarries and Owen Farrell added 16 points with the boot to set up a home quarter-final tie.
Edinburgh, meanwhile, advanced to the knockout stage for the first time in eight years when they produced some scintillating rugby to sweep aside London Irish 34-11.
The Scottish outfit's passage was secured by tries from Tim Visser, Jim Thompson, Netani Talei and Lee Jones, plus a string of kicks from captain Greig Laidlaw, who landed all four conversions and a brace of penalties.
The Exiles, who had no chance of progressing from Pool Two, posed a limited offensive threat. Their points came from a Jonathan Joseph try and two penalties by Adrian Jarvis.
Earlier speed king Takudzwa Ngwenya scored a blistering hat-trick of tries as Biarritz dumped Ospreys out of the competition.
Zimbabwe-born United States international Ngwenya, regarded as one of the fastest men in world rugby, was in superb form during a one-sided 36-5 rout against opponents unable to deal with his pace.
Left-wing Benoit Baby and impressive former England full-back Iain Balshaw got their other touchdowns with scrum-half master tactician Dimitri Yachvili racking up 11 points through four conversions and a penalty.
Ospreys had the dominant scrum but little else with their only score coming when replacement hooker Richard Hibbard pounced on a Biarritz line-out blunder for a try.
Cardiff Blues booked their quarter-final place in the day's other game with a 36-30 victory over Racing Metro 92.
The Blues have an away tie against holders Leinster - thanks to wing Alex Cuthbert's try double, a Lloyd Williams touchdown and 21 points from full-back Leigh Halfpenny, including five penalties.
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