Georgia star Kvaratskhelia celebrated becoming a dad on Wednesday by netting Napoli's second with 15 minutes remaining in an absorbing contest at the Stadio Diego Armando Maradona.
But while his deflected strike ensured Napoli of the three points and redemption after last weekend's humbling at Verona, Kvaratskhelia's real touch of class came in stoppage time at the end of the first half.
The 23-year-old, who also hit the crossbar, clipped a delightful pass over the Bologna defence for the onrushing Giovanni Di Lorenzo, who lashed home the opening goal and unleashed joy both in the stands and on the touchline.
"I think you saw it on the pitch, the energy, and I did everything for the team," said Kvaratskhelia to DAZN.
"This week was for me so important, I'm so happy that I also came here and won with the team. I'm so happy."
Napoli captain Di Lorenzo was heavily criticised after his dire performances at Euro 2024, where Italy were dumped out as reigning champions in the quarter-finals by Switzerland.
But his goal helped Napoli beat an enterprising Bologna team who should have more than the one point that they have collected from their first two matches.
"These fans show me a lot of love and I try to pay that back every time I step out onto the pitch," said Di Lorenzo.
Substitute Giovanni Simeone made it a brilliant home debut for Conte when he forced home new signing David Neres' low cross deep in added time.