After beating holders Liverpool in their opening Group E game, coach Carlo Ancelotti left out Lorenzo Insigne and dropped Dries Mertens to the bench against the Belgian champions
Genk had conceded six goals in their opener against Salzburg.
Arkadiusz Milik made only his second start of the season in attack and his rustiness showed as he struck the woodwork twice.
He also missed three more good chances from close range as the home side led a charmed life in front of their own supporters.
Napoli defender Kalidou Koulibaly, who moved from Genk to Napoli five years ago, had an effort from a corner kick cleared off the line just before half-time.
Team captain Jose Callejon missed from close range early in the second half.
Mertens, one goal shy of equaling Diego Maradona’s record of 115 for Napoli, was brought on just before the hour mark.
He took 15 minutes to get into the game before being denied with two quick efforts.
With seven minutes left, a slip in the Napoli defence presented Ianis Hagi, son of the Romanian great Gheorghe, a chance to score.
But he fired his effort over from inside the penalty area.(Reuters/)
(Edited by Dianabasi Effiong and Olawale Alabi)