Clermont receive fellow Top 14 side Racing Metro 92 at Stade Marcel Michelin in round six. Racing beat them at home in round one, but have not won a game since then.
"A home quarter final definitely helps and that will be our aim and ambition next week. We have qualified now and that's positive," said Clermont coach Vern Cotter.
"Next week we have a big game against our rivals Racing Metro, which will be a stern test for us at home, and hopefully we can get a few more points and be in a better position in the play-offs."
Harlequins pushed Clermont all the way at the Twickenham Stoop and led early on thanks to a great piece of skill from England scrum half Danny Care that paved the way for a Matt Hopper try.
But the current leaders of the Top 14 hauled themselves back into the contest with Napolioni Nalaga's 23rd Heineken Cup try in 28 games and went on to record their seventh successive away win in Pool matches.
"We weren't particularly efficient in the first half, we had a couple of scoring opportunities and missed them and I was worried that we wouldn't get many in the game and we squandered those two," added Cotter.
"But we managed to come back and wear them down and then we did get opportunities in the second half and we managed to score from them. It was a tight game, I would have liked to have won the last scrum and not gone through the last 20 seconds nervously.
"The boys readdressed things at half-time and we wanted to play the game down in their half which we did. Then we applied more pressure and get some points.
"We had to try and relax, be more composed and stick to a plan we wanted to put in place. Even then I think we lost a lot of ball in the second half but managed to score the last try, which gave us a bit of breathing space and enabled us to get the win."