Bath captain Francois Louw scored a try and created another as his side ran out 35-18 victors at the Stade Ernest-Wallon.
The Springbok flank was in sensational form and was on hand to round off a superb try in the 70th minute as Bath moved to within one point of Toulouse at the top of Pool 3 with just next weekend's matches remaining.
Mike Ford's side had earlier raced into a 25-7 half-time lead courtesy of some scintillating attacking rugby as Matt Banahan, Chris Cook and Jonathan Joseph all crossed for tries.
Meanwhile, the Glasgow Warriors kept up the pressure on the top two in the pool as South African-born wing DTH van der Merwe claimed a hat-trick in a 21-10 victory over Jake White's Montpellier.
In Sunday's other matches Racing Métro and the Northampton Saints eased past Treviso and the Neath-Swansea Ospreys respectively to set up a winner-take-all encounter at Franklin's Gardens next weekend.
Sunday results:
Glasgow Warriors 21 Montpellier 10
Toulouse 18 Bath 35
Racing Métro 53 Treviso 7
Ospreys 9 Northampton Saints 20
Friday and Saturday results:
Leicester Tigers 40 Llanelli Scarlets 23
Saracens 33 Munster 10
Toulon 55 Ulster 20
Leinster 50 Castres 8
Sale 13 Clermont 22
Harlequins 3 Wasps 23
Photo: Pascal Pavani/Getty Images
