Napoli loses to Bologna in Italian Cup
It is the second time in a week Napoli has lost to Bologna, following Sunday's 3-2 defeat in the league, in which Kone also scored.
Edinson Cavani headed Napoli in front in the 12th minute before Cristian Pasquato equalized seven minutes from halftime.
After the goal, Cavani and coach Walter Mazzarri held up a Napoli shirt with the words ''Cannavaro and Grava'' written on it, in support of captain Paolo Cannavaro and defender Gianluca Grava, who were each banned for six months on Tuesday for failing to report match-fixing.
Napoli was penalized two points in Serie A in the same case.
Napoli is the only side currently in the top eight of the Italian league that has not advanced to the quarterfinals. Bologna will play Inter Milan.
Earlier, Lazio beat Siena 4-1 on penalties to book its place against Catania.
Siena appeared to be heading for the next round, in new coach Giuseppe Iachini's first match in charge, after a comedy own goal 10 minutes into the second half.
Lazio goalkeeper Juan Pablo Carrizo did well to deny Francesco Valiani but defender Michael Ciani's attempted clearance then crashed off teammate Lorik Cana and into the net.
However, Ciani atoned for his error by heading in an equalizer in the fifth minute of stoppage time.
Siena missed several chances in extra time before Simone Vergassola and Marcelo Larrondo had their spot kicks saved in the shootout.
Fiorentina will face Roma after a 1-0 win over Udinese.
Borja Valero capitalized on an error from Dusan Basta to score the only goal of the game in the 36th minute.