Clermont overpowered Saracens and fly-half Brock James exorcised his own Heineken Cup demons with 17 points after coming on as a third-minute replacement.
Wales full-back Lee Byrne scored the only try of the match after Nathan Hines and Aurelien Rougerie had combined to create the opening.
Clermont will face defending Heineken Cup champions Leinster in a titanic semi-final in Bordeaux on April 29, the day after Ulster tackle Edinburgh for a place in the Twickenham final.
Exeter, Harlequins and Wasps all lost to French opposition in the Amlin Challenge Cup this weekend and Saracens' Heineken Cup ambitions also disappeared across the Channel.
For only the third time in the history of English clubs' involvement in the Heineken Cup there will be no Aviva Premiership representatives in the semi-finals.
Saracens, the Premiership champions, could not live with Clermont's physicality and James buried memories of his Heineken Cup quarter-final nightmare from 2010.
On that occasion, the Australian choked in front of goal and his two fluffed drop goal attempts at the death gifted victory to Leinster.
But James pulled the strings expertly on Sunday after replacing David Skrela, landing four penalties, a conversion and a drop goal to thrill the estimated 2,000 travelling supporters.
Vicarage Road was a riot of noise and colour before kick-off but the home support among the 11,047 crowd soon fell silent as Clermont turned on the power.
Skrela was injured in a tackle on Brad Barritt but James brought an accurate tactical kicking ability and he repeatedly pinned Saracens back, creating a platform for the destructive Clermont pack.
Saracens struggled for most of the first half to live with the French champions' scrummaging power, with Rhys Gill and Matt Stevens both penalised.
James kicked Clermont into a seventh-minute lead and then launched a high kick for Rougerie to chase into the Saracens 22, leaving David Strettle with no option but to concede the five-metre scrum.
Clermont turned on the power again to win the penalty and when Morgan Parra tried to take a quick tap penalty he was pole-axed by a no-arms tackle from Charlie Hodgson.
James slotted the subsequent penalty and extended Clermont's advantage again after Gill, the Saracens loose-head prop, had been penalised at the scrum.
Saracens' famed defensive character was being tested with Georgian prop Davit Zirikashvili crashing the ball up and New Zealand wing Sitiveni Sivivatu a constant threat in the loose.
James missed two shots at goal after Farrell had kicked what turned out to be Saracens' only point of the day and the home side finished the first half positively, earning two scrum penalties.
But any hope of a Saracens comeback in the second half were erased within four minutes of the restart when Hines offloaded to Rougerie, who cut a brilliant angle to create a four on one overlap.
Parra took the ball on, drew the stranded Saracens full-back Alex Goode and sent Byrne clear for the try, which James converted and then followed up with a sweetly taken drop goal and a fourth penalty.
In the first hour, Saracens made just one trip to the opposition 22 as Clermont's aggressive defence closed down their attacking options.
It was not until the French giants were out of sight that Mark McCall's side were able to build any pressure.
Saracens dominated the final 20 minutes, pitching camp on the Clermont try-line but the visitors defended with great character and refused to yield.
Strettle came close to wriggling over but Clermont scrambled brilliantly, defending with the same power and character with which they had attacked Saracens in the first hour.
Clermont's victory sealed their first appearance in the Heineken Cup semi-finals.