The remaining two spots will be decided on Sunday with several teams including former champions Leicester and Wasps still in the equation.
Biarritz claimed a 26-19 bonus-point win over Bath to secure top spot in Pool Four and a home quarter-final while Bath bow out of European action.
Stuart Hooper handed Bath a glimmer of hope but it was short-lived with Takudzwa Ngwenya racing clear for the bonus-point try after 63 minutes.
Tom Biggs struck with two tries for Bath in the last 10 minutes but it was not enough.
Ulster secured their place in the last eight for the first time in 11 years with a 43-6 bonus-point victory over Aironi at Stadio Luigi Zaffanella.
Number eight Pedrie Wannenburg scored twice in a man-of-the-match display while tries from Andrew Trimble, Chris Henry and a penalty try wrapped up a bonus point before Simon Danielli capped the victory with a late score.
Fly-half Ian Humphreys also booted 13 points, including the opening points of the game with a third-minute penalty to help settle Ulster nerves.
Castres 12-23 Northampton
Northampton secured a home tie in the quarter-finals with a comfortable 23-12 victory over an under-strength Castres at Stade Pierre-Antoine.
Tries from man-of-the-match Joe Ansbro, Phil Dowson and Ben Foden ensured the Saints go through to the knock-out stage as one of the top four seeds, as well as recording a 100% record in Pool One - the first English team to do so since Bath in 2002.
Edinburgh 14-21 Cardiff Blues
Five penalties from the boot of Leigh Halfpenny helped Cardiff Blues round out their campaign with a 21-14 victory over Edinburgh at Murrayfield.
The Wales winger's haul was added to by six points from Dan Parks but the win was not enough for the Blues to give themselves a chance of a place in the last eight of the second-tier Amlin Challenge Cup.
Edinburgh registered the only try of the game through centre Ben Cairns, with Chris Paterson adding nine points with the boot, but they end another hugely disappointing European campaign at the bottom of the pool.
Munster 28-14 London Irish
Munster scored three converted tries in the final 10 minutes to break clear of London Irish and earn a confidence-boosting 28-14 bonus-point win.
Irish were just 12 minutes away from becoming only the second team to beat Munster in a Heineken Cup tie at Thomond Park.
Their captain Seilala Mapusua scored a try and set up the second for Sailosi Tagicakibau as the visitors edged into a 14-7 lead. But Munster, who are Amlin Challenge Cup-bound now, hit back decisively with late tries from Niall Ronan, Keith Earls and replacement Darragh Hurley.
Ospreys 29-17 Toulon
Wales wing Shane Williams came off the replacements' bench for his first game in 10 weeks to inspire a lacklustre Ospreys to a 29-17 victory over Toulon at the Liberty Stadium.
The Ospreys, who had already failed to reach the knockout stages, looked likely to lose to the French pool winners until Williams entered the fray just before the hour mark, creating a score for fellow wing Nikki Walker just five minutes later.
Alun Wyn Jones also touched down for the hosts, with Dan Biggar and James Hook kicking the rest of their points. Rory Lamont and Matt Henjak were the try-scorers for Toulon, with Jonny Wilkinson contributing seven points.