Diego Perez setting up Di Vaio for the opening goal after 37 minutes. The former Italy international extended the lead moments later after pouncing on a defensive error to slot in his second and give his side a 2-0 half-time lead.
Inter continued to battle but were left open to the counterattack in the second half and Bologna put the game beyond doubt when Acquafresca fired home from the edge of area.
An Edison Cavani brace and Ezequiel Lavezzi strike gave Napoli a 3-0 win over Fiorentina in Friday's other match.
Uruguay international Cavani opened the scoring after just three minutes at Stadio Artemio Franchi before doubling up 10 minutes after the break.
Argentine Lavezzi struck in injury time to seal a second consecutive win for Walter Mazzarri's side
