Clermont saw off a spirited Leicester Tigers side 22-16 at Parc des Sports Marcel Michelin on Saturday, securing themselves a European semi-final.
Wesley Fofana's try and the boot of Parra gave the French outfit a 19-7 lead they thoroughly deserved at the interval.
Leicester's response in the first half came through Jordan Crane's touchdown and Owen Williams added three penalties after the break to reduce Auvergne's advantage.
But Parra's fifth three-pointer proved decisive as the hosts held on to move into the last four in Europe.
Having gone into the game with a 74-match unbeaten run at home, Clermont were rightly considered favourites, but they have struggled over the previous couple of weeks.
They were also without the influential Sitiveni Sivivatu on the wing, but it didn't seem to hamper Vern Cotter's men who started impressively.
Although Leicester had a chance early on through Manu Tuilagi, the hosts asserted their control and Parra took them into a 3-0 lead after 14 minutes.
Clermont continued to dominate and deservedly scored the first try of the afternoon when good work from Aurelien Rougerie and Davit Zirakashvili sent Fofana over.
Leicester struggled to get any headway in the match as Clermont's sheer physical presence overpowered the visitors, and their scrum-half duly rewarded their excellence with two successive three-pointers.
However, against the run of play, the Tigers worked a superb try to give them hope. Williams' well-judged kick put Jamie Gibson in space and the back-rower combined with Blaine Scully to send Crane across the whitewash.
Cotter's side came back, though, and Parra's fourth penalty took them 19-7 ahead at the break.
Richard Cockerill's team opened the second period impressively and Williams' long-range effort from the tee reduced the deficit to nine points.
The Welsh fly-half was on target again soon after as the Midlands' outfit continued to eat into the Auvergne lead. All of a sudden, the hosts were feeling the pressure.
Two penalty chances from their half-backs went awry and Williams, for the third time in the half, was on target via the boot to make the score 19-16.
But Clermont's driving game, a constant threat throughout, remained strong and, following another collapsed maul, Thomas Waldrom was sin-binned. Parra converted the resultant opportunity and, despite late pressure, the Top 14 team held on.
Pen: Parra 5
Pen: Williams 3
Clermont: 15 Jean-Marcellin Buttin, 14 Noa Nakaitaci, 13 Aurelien Rougerie (c), 12 Wesley Fofana, 11 Naipolioni Nalaga, 10 Brock James, 9 Morgan Parra, 8 Fritz Lee, 7 Damien Chouly, 6 Julien Bonnaire, 5 Nathan Hines, 4 Jamie Cudmore, 3 Davit Zirakashvili, 2 Benjamin Kayser, 1 Thomas Domingo.
Replacements: 16 Ti'i Paulo, 17 Vincent Debaty, 18 Clément Ric, 19 Julien Piere, 20 Alexandre Lapandry, 21 Thierry Lacrampe, 22 Mike Delany, 23 Benson Stanley.
Leicester: 15 Matthew Tait, 14 Blaine Scully, 13 Manu Tuilagi, 12 AnthonyAllen, 11 Niki Goneva, 10 Owen Williams, 9 Ben Youngs, 8 Jordan Crane, 7 Julian Salvi, 6 Jamie Gibson, 5 Ed Slater (c), 4 Louis Deacon, 3 Logovi'i Mulipola, 2 Tom Youngs, 1 Marcos Ayerza.
Replacements: 16 Rob Hawkins, 17 Boris Stankovich, 18 Fraser Balmain, 19 Graham Kitchener, 20 Thomas Waldrom, 21 David Mele, 22 Toby Flood, 23 Scott Hamilton.
Referee: Alain Rolland (Ire)
Assistant referees: George Clancy, David Wilkinson (both Ire)
TMO: Simon McDowell (Ire)