Too little too late for Bath
However, the final score in Llanelli – a 30-27 win by the Scarlets over Toulon – denied the West Country side a place in the knockout stages.
Tom Dunn, Matt Banana, Anthony Watson, Jonathan Joseph, Zach Mercer and Luke Charteris all scored as well as Bath being awarded a penalty try as they did all they could.
But, with both Scarlets and RC Toulon coming away with points in Wales, it meant Bath finish third in Pool Five and are eliminated from the competition.
Hosts Benetton raced out of the blocks as wing Luca Sperandio opened the scoring, but the Bath riposte was immediate, with hooker Dunn crashing over the whitewash just three minutes later.
French referee Pascal Guazere would then award Bath a penalty try as they asserted pressure on the Benetton defence and when flyers Banahan and Watson slid home, the tourists were assured a bonus point, only for Joseph to add a fifth before the interval.
Benetton returned from the break rejuvenated and started their fightback as Sebastian Negri and Tommaso Benvenuti scored tries within four minutes of each other.
But the match belonged to Bath in Treviso with forwards Mercer and Charteris adding the gloss to a emphatic away triumph by forcing their way to tries, yet Benetton had the final say as Monty Ioane snatched a late bonus-point score for the hosts.
Tries: Sperandio, Da Oleggio, Benvenuti, Ioane
Cons: Allan 4
Tries: Dunn, penalty try, Banahan, Watson, Joseph, Mercer
Cons: Burns 5, penalty try does not require a conversion
Yellow card: Edoardo Gori (Benetton, 22)
Benetton: 15 Ian McKinley, 14 Tommaso Benvenuti, 13 Luca Morisi, 12 Alberto Sgarbi, 11 Monty Ioane, 10 Tommy Allan, 9 Edoardo Gori, 8 Robert Barbieri, 7 Seb Negri Da Oleggio, 6 Whetu Douglas, 5 Dean Budd, 4 Ira Herbst, 3 Marco Riccioni, 2 Tomas Baravalle, 1 Nicola Quaglio.
Replacements: 16 Hame Faiva, 17 Alberto de Marchi, 18 Simone Ferrari, 19 Federico Ruzza, 20 Alessandro Zanni, 21 Braam Steyn, 22 Giorgio Bronzini, 23 Luca Sperandio.
Bath: 15 Anthony Watson 14 Matt Banahan 13 Jonathan Joseph 12 Ben Tapuai 11 Aled Brew 10 Freddie Burns 9 Kahn Fotuali’i 8 Zach Mercer, 7 Sam Underhill, 6 Matt Garvey (captain), 5 Elliott Stooke, 4 James Phillips, 3 Henry Thomas, 2 Tom Dunn, 1 Lucas Noguera.
Replacements: 16 Michael van Vuuren, 17 Nick Auterac, 18 Max Lahiff, 19 Luke Charteris, 20 Paul Grant, 21 Darren Allinson, 22 Josh Lewis, 23 James Wilson.
Referee: Pascal Gauzère (France)
Assistant referees: Laurent Cardona (France), Jean-Luc Rebollal (France)
TMO: Eric Gauzins (France)