Les Jaunards kept their double hopes alive a month after lifting the European Challenge Cup in Newcastle.
Liam Gill put Lyon in front with a try 15 minutes in, but Greig Laidlaw was on target with three penalties before Damian Penaud touched down for a try that the Scotland captain converted to make it 16-8 at the break.
Alivereti Raka added a second Clermont try just after Lyon prop Clement Ric had been shown a yellow card, but Deon Fourie finished at the other end.
Fourie's score came after Camille Lopez's departure to the sin bin, giving Lyon hope of pulling off a fightback.
But it was not to be as George Moala went over after another Laidlaw penalty and Clermont set up a showdown between the regular season's top two at Stade de France next weekend.