Napoli s Nigeria s forward Victor Osimhen celebrates after winning the UEFA Champions League Group A football match between SSC Napoli and Ajax Amsterdam at the Diego Armando Maradona Stadium in Naples on October 12, 2022. AFP
The Italian club is atop both Serie A and its Champions League group and unbeaten in both competitions.
Napoli was in firm control and 2-0 up within 16 minutes thanks to goals from Hirving Lozano and Giacomo Raspadori. Davy Klaassen pulled one back at the start of the second half but Kvaratskhelia restored Napoli's cushion from the penalty spot.
Steven Bergwijn also converted a late penalty for Ajax before substitute Victor Osimhen sealed the result on his comeback.
Ajax, which lost 6-1 at home to Napoli last week, will be glad to see the back of the Italian team.
Napoli maintained its perfect record in the Champions League and moved six points above second-placed Liverpool, which was playing at Rangers later. Ajax was three points below Liverpool.
Napoli got off to the perfect start at the Stadio Diego Armando Maradona as it took the lead in under four minutes. Piotr Zielinski started the move and helped end it when Lozano played a pass to him before continuing his run and nodding the return past goalkeeper Remko Pasveer.
Kvaratskhelia almost scored a stunning second before helping Napoli double its lead in the 16th minute with a run down the left and a cross for Raspadori to blast in for his fourth Champions League goal in three matches.
Ajax halved the deficit four minutes after the break as Klaassen headed in Calvin Bassey's cross but Napoli restored its two-goal advantage in the 62nd when Kvaratskhelia fired a penalty into the top left corner after Jurrien Timber charged down a shot with his arm.
Ajax had a spotkick of its own seven minutes from time after Juan Jesus was adjudged to have hauled down Brian Brobbey. Bergwijn confidently converted.
Osimhen was desperate to score on his first appearance after more than a month out with injury and he did so in stoppage time as his persistence paid off when he stole the ball off the Ajax defender Daley Blind and fired into the empty net.
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