Jan Bednarek headed the hosts in front from a corner in the 11th minute, but Scott McTominay equalised shortly before half-time. Gabri Veiga restored Porto's advantage in the 71st minute, Jakub Kiwior made it 3-1 from another corner ten minutes later, and Samu Aghehowa converted a late penalty after Rafa Marín was sent off.
Farioli was particularly pleased to give the home supporters a memorable evening after Porto had struggled to turn their performances in the opening three league-phase matches into points.
"It was important. I think we all had this desire to give our fans such a special night, especially after three games where we did okay but unfortunately weren't good enough to materialise what we did into points," the Porto coach said.
The Italian also credited the work on the training ground and the commitment of his players for their effectiveness from dead-ball situations.
"We work a lot. We have a big coaching team who is always looking for small details, plus the dedication from the players, with good kicks and good headers."
Porto had started strongly and could have extended their lead before McTominay's equaliser, but Farioli felt his team responded impressively after the break.
"We did everything that we could. We started very strong. After the first goal, we had the chance to score the second a bit earlier. We dropped a bit at the end of the first half and paid the price against a side of this quality."
He added: "But second half was great, a lot of chances. A great game from all who played and it was great to win in front of our fans."
Napoli coach Massimiliano Allegri was disappointed by the result, particularly the manner in which his side conceded, but refused to criticise his players.
"We conceded two goals from set-pieces and they were very good. These are details that make the difference. We conceded the second goal from our own goal kick and could have done better. We played a good game for 70 minutes. I'm not angry, but disappointed and frustrated with the situation. I have nothing to reproach the players for tonight, in terms of their dedication and desire."
Allegri felt Napoli had performed well physically and technically, but acknowledged that Porto had taken advantage of their mistakes.
"We have to analyse and improve our defending from set-pieces."
The defeat leaves Napoli with plenty to address, while Porto can take confidence from a performance that finally delivered the points Farioli felt their earlier efforts deserved.