English champions Northampton stunned South African franchise Bulls in Pretoria 30-21 in Pool 3
In Pool 2, Leinster eked out a 15-7 home win over Clermont for a second straight victory and La Rochelle pulled away from Bristol to win 35-7.
Stormers, like their compatriots Sharks, rested a host of players for their trip to wintry England and were crushed 53-16 by Harlequins in Pool 4.
Bordeaux-Begle handed Ulster, the 1999 champions, a second beating in successive weeks from French opposition, following a drubbing in Toulouse.
Japanese international number eight Tevita Tatafu crashed over after two minutes for the visitors with former Ireland fly-half Joey Carbery adding the conversion.
Ulster hit back with tries for Cormac Izuchukwu, Nick Timoney and Werner Kok to lead 19-14 at the break but crumbled in the final quarter as the visitors ran in four tries through French wings Damian Penaud and Louis Bielle-Biarrey, lock Guido Petti and Ugo Boniface.
"We put a huge effort in first half and we ran out of steam a wee bit," said Ulster assistant coach Dan Soper.
"They had a lot of power come off their bench in the last quarter and we weren't able to handle that."
While Leicester suffered a beating in the first round, the Durban-based Sharks had won comfortably at home against another English club Exeter.
But the South Africans, who face the Bulls in the United Rugby Championship next weekend, brought a depleted squad to the English Midlands, leaving, notably, Siya Kolisi, Eben Etzebeth and Bongi Mbonambi at home.
Julian Montoya gave the hosts a ninth minute lead. Manu Tshituka replied for the visitors after 20 minutes but the Tigers then scored four tries in 15 minutes -- through Montoya, Ollie Haskell-Collins, Solomone Katato and Handre Pollard -- to secure a bonus point before half time.
'Soaking up the sun'
After the break Jack van Poortvliet, Charlie Clare and Emeke Ilione all scored for Leicester. Ethan Hooker, who plays centre, replied for the Sharks. Leicester converted all eight tries and South African Pollard finished with 20 points.
Pollard told broadcaster Premier Sports he had chatted to fellow Springboks ahead of the match.
"I had a big chat to the boys early in the week, they're soaking up the sun, getting ready for a big derby next week," Pollard said.
In London, only two players who started as Stormers lost at home to Toulon in round one were in the first XV. Harlequins, narrow losers in Paris in the opening week, made their visitors pay scoring eight tries, with skipper Alex Dombrandt and Cadan Murley both grabbing hat-tricks.
Quins jumped from last to first in Pool 4.
In Dublin, Alivereti Raka gave Clermont a fourth minute lead, but Garry Ringrose and Jordie Barrett replied with two tries in four minutes midway through the half. That ended the scoring, apart from a solitary 48th minute Leinster penalty by Sam Prendergast.
La Rochelle scored five tries to see off visiting Bristol. They have scored one more try and have a one-point edge in points differential over Leinster and top the Pool 2.
Northampton pulled off a remarkable bonus-point victory as they beat Bulls 30-21 at Loftus Versfeld where the 30C heat was in stark contrast to conditions in England.
Saints, who hammered Castres in their opening match, were second best in possession and territory. But they counter-punched to run in four tries in this Pool 3 encounter, two of them by wing Tommy Freeman.
Northampton have a maximum 10 points from their opening two games and top Pool 3 while Bulls have lost twice to English opposition after stumbling at Saracens a week ago and sit last.
