Bordeaux left it late against Ulster in their European Champions Cup opener, with hulking prop Sebastien Taofifenua sparking a three-try finish for a 28-13 victory on Sunday.
Ireland fly-half Ian Madigan opened the scoring for Bordeaux with a third-minute penalty.
But in a scrappy opening quarter, it was Ulster who first crossed the whitewash thanks to a simple two-phase set-piece move, Stuart Olding's crashball quickly reworked for skipper Andrew Trimble to sprint through unfettered.
Jackson got the extras and booted a penalty just before half-time after No.8 Loann Goujon's attempted pick-up from the base of a scrum floundered as the pitch cut up and bounced the ball beyond his reach.
Madigan hit his second penalty early in the second half, followed by a third by Lionel Beauxis, before Jackson pulled one back.
But then came the thrilling denouement in the Pool 5 game.
With seven minutes to play, Taofifenua, weighing in at 130kg (20st), used his immense ballast to squirm past Trimble, Ruan Pienaar and Rory Best and dot down in the corner.
Then came a penalty try after Fijian flyer Metuisela Talebua was taken out after breaking free and gathering his own chip ahead with the line beckoning.
The icing on Bordeaux's cake was provided by Australian winger Blair Connor, who sprinted the length of the field for a memorable try after full-back Jean-Marcellin Buttin sparked an attack from his own tryline.
"We dominated the second-half because we had possession," said Bordeaux forwards coach Jacques Brunel.
"Everything's less tiring when you've got the ball.
"We were less under the cosh and found ourselves on top and that helped us with the job in hand."
The Pool 1 match between last season's beaten finalists Racing 92 and Munster was postponed after the death of the Irish province's head coach Anthony Foley.
The day's other game sees Exeter host French giants Clermont, also in Pool 5.