David Strettle was the hero for the French side, scoring two brilliant tries, with centres Aurelien Rougerie and Wesley Fofana also getting over the line.
Fly-half Camille Lopez kicked 10 points while Morgan Para added two conversions. But the visitors registered tries through Justin Tipuric, Eli Walker, Sam Parry and Tom Habberfield, with Dan Biggar slotting three conversions and a penalty, to pick up two valuable bonus points.
Biggar hailed the bravery of Ospreys: “I thought we showed a tremendous amount of bravery,” said Wales fly-half Biggar, who kicked nine points as his side held on to top spot in the standings.
“We knew coming here that it would not be enough to just play for penalties and drop goals. We had to be positive, we had to be confident enough to play and try and put them under pressure.
“We did that but they stood tall towards the end of that first half and we could easily have let things slide away there.
“But we knew we had to keep playing our game and chance our arm. It if had ended with us losing by 40 points then at least we would know we had given it a go.
“We managed to get the balance right and took our chances well. We could have dropped our heads and it is a huge testament to our spirit that we finished those chances at the end.
“To come away from one of the most difficult place to play in Europe with two points is like a win for us, really.”
Clermont had had to wait for their campaign to get under way as their opening game against Bordeaux-Begles was postponed in the wake of the Paris terror attacks, but coach Franck Azema was happy with their start.
He said: “For sure there are things for us to work on but a bonus-point win is the perfect way for us to start this campaign and we scored some good tries.
“We would rather not have let them get the two points at the end, but we can now look towards two important games against Exeter next month.”
Tries: Strettle 2, Rougerie, Fofana. Cons: Lopez 2, Parra 2. Pens: Lopez 2.
Abendanon, Strettle, Rougerie, Fofana, Nakaitaci, Lopez, Parra, Domingo, Kayser, Zirakashvili, Cudmore, Vahaamahina, Chouly, Lapandry, Lee. Replacements: Vulivuli for Nakaitaci (72), James for Lopez (58), Radosavljevic for Parra (76), Chaume for Domingo (62), Kotze for Zirakashvili (62), Van der Merwe for Vahaamahina (54).
Tries: Tipuric, Walker, Parry, Habberfield. Cons: Biggar 3. Drop Goals: Biggar.
D. Evans, Grabham, Spratt, Matavesi, Walker, Biggar, Leonard, James, Baldwin, Arhip, Ashley, Jones, Lydiate, Tipuric, King.
Davies for Grabham (68), Habberfield for Leonard (59), Bevington for James (72), Parry for Baldwin (47), Baker for King (62).
George Clancy (Ireland).