Georgia winger Kvaratskhelia lashed in the opening goal on the hour mark after spellbinding dribbling left Atalanta’s defence wondering which way to look before the ball finished in the back of the net.
His 11th league strike of the campaign set Napoli on their way to stretching their lead on Inter Milan who fell to a shock 2-1 defeat at lowly Spezia on Friday.
Lazio could have risen to second and trimmed the lead to 17 points in the late game on Saturday but played out a 0-0 draw in Bologna to remain third.
In Naples, Amir Rrahmani made sure of the points with 13 minutes remaining with a towering header from substitute Eljif Elmas’ corner.
“We’re enjoying ourselves, we’re playing well even if it was difficult to begin with tonight because Atalanta are a good team,” Rrahmani told DAZN.
“Of course we say it’s normal, we’re in a situation in which you can see with our fans how much they can feel it.”
Lazio can cut the yawning gap between Napoli and the rest to 17 if they win at Bologna in Saturday’s late match and take second spot.
But it’s surely only a matter of time until southern Italy’s biggest club win the Scudetto for the first time since 1990, when Diego Maradona was still strutting his stuff in sight of Mount Vesuvius.
Kvaratskhelia was key to what ended up being a straight-forward win but been a nervy affair following their home defeat to Lazio last weekend.
Before he struck Napoli had struggled to create opportunities, Serie A’s leading Victor Osimhen going closest shortly after the break with a ambitious bicycle kick and header from a corner.
And they needed Pierluigi Gollini, on loan from Atalanta, to be at his best to deny decent efforts from Luis Muriel and Duvan Zapata before Rrahmani sealed the points.
Napoli now turn their attentions to the visit of Eintracht Frankfurt on Wednesday, a 2-0 first-leg lead to protect and a debut spot in the Champions League quarter-finals within their grasp.
“When you come to Naples you enter into the history, what the people want, the feeling for the team that can become pressure,” said Spalletti.
“You need to have imagination and believe that you can win.”
A third defeat in four matches will likely damage Atalanta’s bid for Europe’s top club competition as they stay sixth and five points behind the top four.
In Bologna, Pedro and Luis Alberto went close for Lazio in the first half while Lewis Ferguson and Musa Barrow hit the woodwork for the hosts.
Lazio could have overtaken Inter and grabbed second place but the draw means they could end the weekend in fifth if the two teams behind them win.
Roma, who sit fourth and host Sassuolo on Sunday, and AC Milan, who are fifth face struggling Salernitana at the San Siro on Monday.
Lazio and Roma meet in the Rome derby next weekend.
Bologna remained in seventh six points behind Atalanta who occupy the last European slot.
Earlier Udinese snapped a six-match winless streak with a 1-0 victory at Empoli.
Andrea Sottil’s team are ninth on 35 points, level with Bologna and Juventus, after just their second win since the start of October.
Empoli stay 14th but are 10 points above Verona who are just inside the relegation zone and host Monza on Sunday.
