The 22-year-old attacker, who impressed at the World Cup in North America, slotted home a right-footed shot into the bottom-left corner on Monday (Tuesday AEST) and could have had two first-half assists and another just before fulltime in a comfortable win.
Volpato's strike and full game comes after the Sydneysider's goal against German side Augsburg and audacious assist against Spain's Celta Vigo earlier this month for Alberto Aquilani's side.
Former Western Sydney and Newcastle defender Mark Natta remained on the bench for Serie B side Cesena, who are coached by ex-Italian international and A-League Men championship-winning Western United forward Alessandro Diamanti.
The Serie A season kicks off on August 23, with Sassuolo at Atalanta a day later.
"The World Cup was the best choice of my life so far, it was an experience that helped me grow a lot," said Volpato.
"I really like the coach's style of play. It's been difficult to assimilate his ideas due to some absences lately, but today it was important to win, also because the season starts here and it gives us confidence.
"We're a young group, I like playing with these guys, I feel a little older."
The opening match of the Championship season for Welsh rivals Cardiff City and Wrexham ended in a thrilling 1-1 draw.
Socceroos midfielder Alex Robertson was subbed off after 80 minutes for the newly-promoted hosts, who scored a ferocious equaliser with almost the final kick of the match.
Wrexham appeared to have derby bragging rights sewn up as the contest ticked into the eighth minute of added time at Cardiff City Stadium.
But George Dobson brought down Joel Colwill on the edge of the box, and his brother Rubin lashed home a brilliant free kick over the wall and Anthony Patterson.
Colwill's strike cancelled out Kieffer Moore's third-minute effort, the forward continuing his habit of scoring against his former employers – his seventh versus the Bluebirds.
Wrexham had 18 goal attempts to 11, but were denied their first win in the capital since 1992.
And in Denmark, former Melbourne City and Wanderers winger Marcus Younis played 71 minutes to help Brondby beat Soenderjyske 3-2 and go top midway through round four.
With PA.
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