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.
Roma crumble
Also on one point are Roma who lost to Empoli at home for the first time in their history after a hugely disappointing display in which Paulo Dybala staying in the Italian capital wasn't enough to inspire Daniele De Rossi's side.
Emmanuel Gyasi's tap-in on the stroke of half-time and a Lorenzo Colombo penalty in the 61st minute sank Roma, who pulled one back through Eldor Shomurodov with 10 minutes remaining but couldn't complete a comeback.
Dybala, whose move to Saudi Arabian outfit Al Qadsiah collapsed on Thursday, was one of three Roma players to hit the woodwork alongside Lorenzo Pellegrini and Gianluca Mancini.
But Roma were booed off the pitch for the way they fell two goals behind against a team which is expected to struggle against relegation.
"We were lacking energy and intensity... We played well in the second half but it wasn't enough, and if you don't play well in the first half things aren't going to well for you," said De Rossi to Sky Sport.
De Rossi doesn't have long to get his team's spirits up as Roma travel to Juventus, who face Verona on Monday, next weekend.
Adams emulates Law
Earlier, Che Adams emulated Denis Law with the decisive goal in Torino's 2-1 win over Atalanta on Sunday, delighting fans who had called for the owner to sell in mass pre-match protests.
Scotland striker Adams netted his first goal for Torino since signing as a free agent last month, tapping home the hosts' second four minutes after half-time.
The 28-year-old became the first of his countrymen to score for Torino since Scotland and Manchester United legend Law in the 1961/62 season.
Adams rolling in the winner after Duvan Zapata's low shot was saved made it a perfect home debut in which he also set up Ivan Ilic's delightful dinked equaliser in the 31st minute.
His strike, and Vanja Milinkovic-Savic saving Mario Pasalic's penalty deep in stoppage time, put Torino on four points from their first two matches.
The win came after thousands of fans marched to the game together to demand that owner and media magnate Urbano Cairo sell the club after 19 largely drab years at the helm.
Fiorentina were held to a goalless draw by Venezia in the day's other early kick-off.
