Ulster were undone by Bordeaux’s finishing power, the French scoring 26 unanswered second half points to consign Richie Murphy’s side to a second straight European defeat.
The final score was Ulster 19, Bordeaux Bègles 40.
In the wake of last Sunday's tanking at Toulouse, this was a hugely damaging result for Ulster as it brought the province four straight defeats in all competitions ahead of next week's home clash with Munster.
Ulster found themselves seven points down after just two minutes of play at Kingspan Stadium.
Tevita Tatafu powered through from a lineout move around the front from a penalty Bordeaux had planted to the corner. Joey Carbery supplied a conversion.
Ulster struck back, making hay of a loose ball in Bordeaux’s 22 allowing Cormac Izuchukwu barrel over and Nathan Doak tie things up on six minutes.
After flanker Marko Gazzotti was yellow carded in the 17th minute, Nick Timoney pirouetted through from a dynamic tap and go to score which Doak converted.
With Bordeaux still down to 14, the French were awarded a penalty try David McCann making his way to the bin, moments after Gazzotti had returned to the action.
More cards shortly followed as prop Jefferson Poirot was binned for kicking the ball out of a ruck in the 31st minute and less than a minute later, Yoram Moefana followed him.
It was 14 versus 13 for a time, but Ulster weren’t able to get the ball over the line from a tap and go and then a move out right when Postlethwaite made a half break.
McCann returned to bring Ulster back to 15 and they finally got the score with the clock in red.
Doak, though, missed the conversion and Ulster trooped off leading 19-14.
The new half began with Bordeaux back up to 15 again, and Ulster on the advance only for McCann’s poor pass to Aidan Morgan to be knocked on by the home team.
Bordeaux finally found a way through just after the hour and though Kieran Treadwell pulled off a great tackle on the left, the French had numbers right allowing Damian Penaud a walk-in.
Penaud supplied an inside pass for lock Guido Petti to break tackles and dot down for the bonus point score. Matéo Garcia converted.
And they weren’t done. Bordeaux broke out with 10 minutes to go, Louis Bielle-Biarrey racing clear to run it in, Garcia to convert. He also kicked the points following Ugo Boniface’s last-minute try.
