Andrew Trimble claimed his 25th Champions Cup try but it was not enough to prevent Ulster from surrendering a late lead to lose 28-13 to Bordeaux-Begles.
Trimble's score helped Ulster build a 10-3 half-time advantage in France and the Irish province were still ahead by four points heading into the final seven minutes.
However, Bordeaux claimed three tries in quick succession to snatch their first win in the opening round of a European Cup campaign and immediately put Ulster on the back foot in a pool that also contains Exeter and Clermont Auvergne.
The home side drew first blood at Stade Chaban-Delmas when f ormer Leinster fly-half Ian Madigan, relishing his battle against Ireland number 10 rival Paddy Jackson, capitalised on some early dominance to kick Bordeaux into a 3-0 lead after just two minutes.
But that early scare sparked Les Kiss' side into life, the visitors battling their way downfield and making the most of their first foray into enemy territory.
The Ulster pack drove the hosts back at a scrum before Stuart Olding charged into midfield. Scrum-half Ruan Pienaar switched the play to the blindside and found Trimble running a devastating angle to cut through and score. Jackson converted to give the visitors a 7-3 lead.
The Belfast outfit had two chances to put themselves even further in charge but twice knocked on close to the try-line. They had to settle for a Jackson penalty late in the first half to make it seven-point lead at the break.
It was Madigan who struck first in the second period with a penalty of his own to cut Ulster's lead back to four points.
Lionel Beauxis then replaced the Ireland outside-half and his first act was to land another penalty that cut the gap to a single point.
But Jackson replied two minutes later with a long-range strike to make it 13-9 and Ulster looked to be on their way to a famous Champions Cup win with some heroic defence.
However, their resolve was finally broken with seven minutes remaining as giant Bordeaux forward Sebastien Taofifenua rumbled over the Ulster defence and squeezed the ball down at the corner to give the hosts the lead.
Metuisela Talebulamaijaina then broke clear and charged downfield from the kick-off before offloading to Baptiste Serin, who was tackled early by Sean Reidy, preventing a try. Referee JP Doyle sin-binned Reidy and awarded a penalty try.
With the game now out of Ulster's reach, Bordeaux added a third try in the final minute when Blair Connor broke free to put the gloss on the hard-fought victory for the TOP 14 outfit.