Napoli lost their 100% record last weekend with a 0-0 draw at Roma after eight successive wins but Luciano Spalletti's side were back to their best against Bologna.
Spanish midfielder Fabian Ruiz opened the scoring in the 18th minute with a fierce left foot drive which eluded Bologna's Polish goalkeeper Lukasz Skorupski.
Napoli were awarded a penalty in the closing minutes of the first half when Chilean defender Gary Medel was penalised for handball as he challenged Victor Osimhen.
Skipper Lorenzo Insigne scored from the spot. Insigne added a second penalty after 62 minutes when Osimhen was fouled.
"I missed a few, but I've always been ready to take the penalties," Insigne told Sky Sport Italia.
"I've never had these problems. Only those who take penalties can miss them. Today, I was calm.
"But the only thing that mattered was to respond to Milan's win (1-0 against Torino on Tuesday)."
Napoli, who are now unbeaten in 16 games at home stretching back to January, have 28 points and lead AC Milan on goal difference.
Champions Inter Milan are third, seven points off the pace.