Ospreys ended Benetton Treviso's run of five successive home wins against Welsh regions with victory in their Pro12 opener at Stadio Monigo.
Scott Baldwin's try after Ospreys opted to kick for an attacking line-out gave the Welsh region a 10-9 half-time lead.
A clever box-kick by Tito Tebaldi was caught by Ben John for a second try.
Four Alberto di Bernardo penalties kept Treviso in touch before Simone Favaro barged over from a rolling maul, but Dan Biggar's boot kept Ospreys ahead.
Christian Loamanu nearly snatched a late try that would have brought Treviso level, with a conversion to follow to win it, but he was hit by a gang of Ospreys tacklers as he went for the line and lost the ball.
Ospreys had named three of their British and Irish Lions on the bench - Richard Hibbard, Adam Jones and Ian Evans - and all three forwards came on in the second half to help combat a powerful Treviso pack.
Treviso: Brendan Williams; Ludovico Nitoglia, Luca Morisi, Alberto Sgarbi, Luke McLean; Alberto Di Bernardo, Edoardo Gori; Michele Rizzo, Michele Rizzo, Leonardo Ghiraldini, Alberto De Marchi, Antonio Pavanello (capt), Valerio Bernabò, Manoa Vosawai, Robert Barbieri, Alessandro Zanni.
Replacements: Giovanni Maistri for A. De Marchi (28), Ignacio Fernandez-Rouyet, Lorenzo Cittadini for Rizzo (51), Dean Budd for V. Bernabo (74), Christian Loamanu, Simone Favaro for Vosawai (50), Fabio Semenzato, Tobias Botes.
Sin Bin: Ghiraldini (22).
Ospreys: Richard Fussell; Ben John, Andrew Bishop, Ashley Beck, Eli Walker; Dan Biggar, Tito Tebaldi; Ryan Bevington, Scott Baldwin, Joe Rees, Ryan Jones (capt), James King, Tom Smith, Joe Bearman, Sam Lewis.
Replacements: Richard Hibbard for Baldwin (61), Duncan Jones for Bevington (62), Adam Jones for Rees (51), Ian Evans for R. Jones (49), Morgan Allen, Tom Grabham for Tebaldi (68), Matthew Morgan, Jeff Hassler,
Sin Bin: Bishop (11).
Referee: Neil Paterson (SRU)
Assistant Referees: Giuseppe Vivarini, Stefano Traversi (both FIR)
Citing Commissioner: Achille Reali (FIR)
TMO: Carlo Damasco (FIR)