Clermont had not been beaten since October, but they were brought back down to earth by Top 14 champions Castres.
Saracens and Racing 92 secured home quarter-finals in the Champions Cup but the hopes of Exeter Chiefs are over after defeat at Munster.
Premiership champions Saracens are through to the last eight of the European Champions Cup after beating Lyon on Sunday.
Racing 92's win over Toulon will not have made pleasant viewing for France coach Jacques Brunel as Teddy Thomas was injured.
The battle between top and bottom in the Top 14 table stayed true to form, Clermont running out comfortable winners on the road.
Stade Francais moved up to fifth in the table as Toulon and Racing 92 ran out convincing winners in Saturday's Top 14 action.
Saracens battled past Cardiff Blues to stay top of Pool 3, while Toulouse came out on top in an entertaining clash with Wasps.
Montpellier's late rally did not deny Top 14 leaders Clermont Auvergne a 28-23 victory, while Guilhem Guirado scored a try in Toulon's win.
There were wins for Clermont Auvergne and La Rochelle in the Top 14 on Sunday.
Lyon scored all five tries in the second half in a rout of Stade Francais, while Racing 92 claimed their fourth consecutive win.
Three-time European champions Toulon have been struggling in the Top 14 and lost to La Rochelle on Sunday.
Felix Lambey and Yoann Huget have been called up to the France squad as replacements for injured duo Bernard Le Roux and Wesley Fofana.
Wasps, without Christian Wade, battled back to draw with Bath, and Edinburgh battered Toulon in Saturday's European Champions Cup action.
Newcastle Falcons' return to Europe's elite club competition was worth the wait as they beat stunning Toulon at Stade Mayol.
Clermont's advantage at the summit of the Top 14 table was reduced to four points after they were beaten at La Rochelle.
Top 14 leaders Clermont Auvergne put some daylight between themselves and second-place Stade Francais on Saturday.