The outcome hinged on the battle between the teams' Scottish kickers, with Wasps' international wing Kenny Logan shading his tussle against Bourgoin's fly-half Mark McKenzie by seven penalties to five.
Toulouse, the inaugural winners in 1996, also look destined for the last eight following a 39-17 win at Padova - their third successive victory in Pool Two.
The Toulouse No 8 Sylvain Dispagne opened the floodgates with a try after two minutes, and further touchdowns followed from Stephan Ougier, Lee Stensness, Cedric Desbrosse and Pierre Boudouy to put the visitors 34- 0 ahead at the interval.
Padova opened their account in the 56th minute when Filippo Rampazzo burst through. Mauro Bergamasco and Brendan Williams also went over to give Padova hope, but Toulouse had the last word when the scrum-half Jerome Fillol crossed with eight minutes remaining.
The Pool Four leaders Munster also made it three wins from three games when they came from behind to win 31-15 in Colomiers. A 10th-minute try by Jason Holland set them on their way, but Colomiers took the lead with tries by the former France full-back Jean-Luc Sadourny and Jerome Sieurac before touchdowns from the Ireland and Lions hooker Keith Wood, Holland and Anthony Horan completed the job for Munster.
The boot of England's fly-half Jonny Wilkinson supplied 25 points as Newcastle romped to a 45-26 win at Dunvant which put them clear at the top of Pool Six in the European Shield.
Sale completed an English double over Welsh opposition by thrashing Caerphilly 51-14 in Pool Three, one of their seven tries coming from the England wing Steve Hanley in his first game back following a double shoulder operation.
Connacht got the better of Toulon 27-13 in Pool Four, while the Wales full-back Shane Howarth contributed 19 points to Newport's 26-10 success over Rovigo in Pool Two. Castres comfortably head that group after their 10-try, 60-25 triumph at Bedford, which featured a hat-trick from Francois Plisson.
Bridgend confounded their domestic form to draw 29-29 in Pool Five with the Allied Dunbar Premiership leaders, Gloucester, who only pulled level with a late try by Ian Sanders. The result, though, was a disappointment for the visitors' director of rugby, Philippe Saint-Andre, who has signed a contract which will keep him at the club until May 2002.
Leeds are the new leaders of Premiership Two after a 54-0 demolition of Waterloo. Worcester are second after slipping up 16-10 at Exeter and Rotherham joined them on the same number of points with a 56-6 hammering of Rugby. The bottom side, West Hartlepool, collected their first win after 12 attempts by upsetting Orrell 23-15.Reuse content