In-demand striker Victor Osimhen opened the scoring towards the end of the first half, shortly after Khvicha Kvaratskhelia missed from the penalty spot, before Frankfurt's top scorer Randal Kolo Muani was sent off just before the hour mark for a late challenge on Andre-Frank Zambo Anguissa.
Napoli then extended their lead less than 10 minutes later courtesy of a well-worked team moved finished off by captain Giovanni Di Lorenzo to put the Italian giants in control of the tie.
Despite an early spell of pressure from Frankfurt, the contest did not spring to life until the final 10 minutes of the first half when Napoli turned the screw and posed a real threat on the host's backline.
Just seconds after Hirving Lozano fired a shot against the inside of the post, Frankfurt defender Buta, unaware of Osimhen rushing towards him, scythed down the Nigerian inside the penalty area as he attempted to clear the ball, and the referee was left with no choice but to point to the spot in the 35th minute.
Kvaratskhelia, who has 12 goals to his name so far this season, stepped up from 12 yards, but Kevin Trapp guessed the right way and dived to his right to tip the ball away from danger to the delight of the Frankfurt faithful.
However, Napoli made amends just five minutes later when Osimhen met a perfectly-weighted curling cross from Lozano to tap home his 20th goal of the season from just a few yards out.
Osimhen thought he had scored an almost identical goal less than a minutes later, immediately from Frankfurt's kickoff, but the Nigerian was caught in an offside position before receiving the pass from Lozano.
Napoli came out the blocks quickly in the second half, with Lozano a constant menace down the right flank, and the Mexican tested Trapp with a powerful shot inside the area on the 55-minute mark, before the German shot-stopper came off his line quickly to deny Kvaratskhelia.
Frankfurt's hopes of a comeback were then dealt a major blow on the 57-minute mark when top scorer Kolo Muani - who contributed with 15 goals and 14 assists in 30 games prior to Tuesday's clash - was shown a straight red card after catching Zambo Anguissa with a high tackle.
Things then went from bad to worse for Frankfurt as Napoli doubled their advantage in the 65th minute in stylish fashion. Following a free-flowing passing sequence, Kvaratskhelia received the ball inside the area before skillfully back-heeling the ball into the path of Di Lorenzo who placed a sweet side-footed strike into the bottom-left corner.
A decent chance fell to Frankfurt's Daichi Kamada eight minutes from time, but the Japanese playmaker failed to generate enough power on his shot inside the box to test Alex Meret between the sticks.
Napoli eventually cruised to a comfortable victory, their fifth in succession without conceding a goal across all competitions, while Frankfurt saw their six-game winning streak on home soil come to an end in the process.
The two teams will now have to wait three weeks until they meet again at the Diego Armando Maradona Stadium for the second leg on March 15.