The Welsh region were indebted to a tries from Eli Walker, Hanno Dirksen (2) and Ashley Beck, while 18 points came from the boot of outside-half Dan Biggar.
Treviso scored two tries through Manoa Vosawai and Luke McLean, while Kris Burton supplied seven points with the boot.
Ospreys’ Pool Two victory was some revenge for their 12-6 defeat at the hands of the Italian side in the opening game of the RaboDirect PRO12.
Treviso suffered a setback when Alessandro Zanni, their 66-cap Italy openside, pulled out just before kick-off with a back injury.
Ospreys scorers: Tries: Walker, H. Dirksen 2, Beck. Cons: Biggar 3. Pens: Biggar 4.
Benetton Treviso scorers: Tries: Vosawai, McLean. Cons: K. Burton 2. Pens: K. Burton.
OSPREYS: Fussell, H. Dirksen, Bishop, Beck, Walker, Biggar, Fotuali’i, Bevington, Hibbard, A. Jones, A. Jones, Evans, R. Jones, Tipuric, Thomas.
Replacements: Webb for Fotuali’i (74), D. Jones for Bevington (64), Jarvis for A. Jones (57), Stowers for A. Jones (76).
BENETTON TREVISO: McLean, Nitoglia, Benvenuti, Sgarbi, Iannone, K. Burton, Botes, De Marchi, Ghiraldini, Roux, Pavanello, Bernabo, Favaro, Derbyshire, Vosawai.
Replacements: Semenzato for Nitoglia (21), Pratichetti for Sgarbi (74), Rouyet for De Marchi (46), Ceccato for Ghiraldini (46), Di Santo for Roux (35), Maistri for Bernabo (74), Minto for Derbyshire (40), Barbieri for Vosawai (74).
Referee Neil Paterson (SRFU).
Results: Amlin Challenge Cup Pool 3: Bayonne 71 Mogliano Rugby 7.
Pool 5: Grenoble 59 Cavalieri Prato 3.