Clermont Auvergne secured their place in the quarter-finals of the Heineken Champions Cup with a 29-13 victory over Ulster at the Stade Marcel Michelin.
Ulster host Bath next weekend where a win would see Dan McFarland's side join Clermont in the last eight.
Tries from Alivereti Raka, George Moala and 16 points from the boots of Morgan Parra and Greig Laidlaw was enough to secure victory form the French side.
John Cooney scored all Ulster's point with a try, conversion and a penalty.
Ulster made a strong start when powerful inside centre Stuart McCloskey burst through the Clermont defence before offloading to Jacob Stockdale who raced up to the 22. The visitors went through the phases but had to settle for three points from Cooney's boot.
Clermont responded well with a well-taken drop-goal from Camille Lopez.
But Ulster had arrived with real intent and a lovely pop pass from Sean Reidy sent tight-head prop Marty Moore clear. Moore offloaded the ball to Cooney who slipped past two defenders for the opening try, which he converted.
Clermont scrum-half Morgan Parra was then sent to the sin-bin for blatantly infringing at the breakdown with Ulster inches from the opposition tryline.
The 14 men of Clermont almost scored a sensational try with a searing break from Raka sending Damian Penaud racing down the touchline. The France wing offloaded to Moala, who appeared to be clear but was thwarted by Robert Baloucoune.
The hosts managed to cut Ulster's lead to a mere point with two penalties from Parra to reduce the deficit to trail 10-9.
Clermont began to flex their muscles in the early stages of the second half, with their scrum winning field position.
The pressure helped them take the lead for the first time in the contest when former All Blacks centre Moala charged into Ulster's 22 to put his side on the front foot. The ball was recycled with Raka stretching to touch down in left corner, with Parra converting from the touchline.
Ulster managed to regain possession and went about building pressure in Clermont's half with a series of driving lineouts.
This allowed Cooney to narrow Clermont's lead to two points with another successful penalty, but it was cancelled out by Parra's boot soon after.
Clermont's scrum possessed the upper hand and after shoving Ulster backwards, Scotland international Laidlaw pushed the hosts out to an eight-point lead.
The French side put the result beyond doubt when Moala smashed his way through the Ulster defence to run in from 35 metres out. Laidlaw improved Clermont's lead from the touchline and there was to be no way back for the visitors.