- Randal Kolo Muani (58')
- Victor Osimhen (40')
- Giovanni Di Lorenzo (65')
In-form Nigeria striker Osimhen, who has now scored 10 goals in his last nine games across all competitions, tapped in at the far post to give his team a 40th minute lead.
Captain Di Lorenzo doubled it from a superb backheel assist by Khvicha Kvaratskhelia, who made amends for his first half penalty miss.
"I am happy with the performance," Napoli coach Luciano Spalletti said. "From the start the team played with character, took control of the game and did what we wanted to do.
"We probably had the chance to score an extra goal that could have been useful for us. I still think it is 50-50 for qualification, because there is still a game to be played.
"We need the utmost humility because when you face a team convinced you have an advantage you can then end up dealing with unexpected situations. Arrogance is the biggest enemy."
They earned a penalty immediately after as Frankfurt's Aurelio Buta kicked Osimhen in his effort to clear the ball.
Georgia forward Kvaratskhelia, who with Osimhen has amassed a total of 32 goals between them in all competitions this season for the runaway Serie A leaders, failed to beat Kevin Trapp from the spot.
Osimhen did it much better only five minutes later after Mexican Lozano, who wreaked havoc down the right wing with his darting runs, whipped in another low cross to the far post for the Nigerian to bundle home.
In doing so, Osimhen became the first Napoli player to score 20 goals in all competitions of a single season since Arkadiusz Milik did it in 2018-19.
Osimhen put the ball in the net again in an almost identical move a minute later but his effort was ruled out for offside.
Close-season signing Kvaratskhelia had a golden chance to double their lead in the 57th but again did not manage to beat Trapp in a one-on-one after another Lozano through ball.
The turning point for Frankfurt came a minute later when their top scorer Kolo Muani got his marching orders for a clumsy challenge on Andre-Frank Zambo Anguissa.
Napoli's pressure grew and they were rewarded in the 65th when Kvaratskhelia picked up the ball in the box and backheeled it for Di Lorenzo to curl a shot into the far bottom corner.
"We still have a second leg to play," said Frankfurt midfielder Mario Gotze. "They scored two goals here, why should we not do that as well? We know everything is still possible."
- Artur Soares Dias