Pepe appeared to have opened the scoring for Porto in the fourth minute, crashing an excellent finish in off the crossbar from a tight angle, but he was denied by the offside flag.
That was a warning for the visitors, and they got another one soon afterwards, as Borja Sainz’s curling effort grazed the top of the bar on its way over.
There was to be no third let-off for the Italians, as Bednarek was left all alone from a corner, nodding a simple header beyond the reach of Alex Meret to take the lead in the 11th minute.
Rasmus Hojlund was among Napoli’s livelier players in the first period, and he nearly scored from a solo counter-attack, driving through multiple tackles from the halfway line and seeing his effort deflected narrowly wide.
Kevin De Bruyne then became the second player to be thwarted by the assistant referee’s flag, finding the back of the net from an offside position.
Having gradually grown into the contest, the visitors found a deserved equaliser before the break, as Scott McTominay hammered home an emphatic finish following a double save from Diogo Costa.
McTominay has now scored seven times in his last nine UCL appearances, which has helped to make him the all-time leading Scottish scorer in the competition.
The home side regrouped at the interval, and Gabri Veiga tested Meret with a shot from the edge of the box in the first meaningful attack of the second half.
Matteo Politano then struggled to sort his feet out from a Porto cross, and the ball fell to Pablo Rosario six yards out, but he could not squeeze the ball past the goalkeeper from close range.
As the pressure mounted, Veiga came agonisingly close to a stunning goal, sending an absolute rocket against the crossbar with Meret well beaten.
There was no surprise about the identity of the scorer when the goal finally came, as Veiga rushed beyond the defence and slid the ball through Meret’s legs to restore the lead.
Having offered very little in the second half before falling behind, Napoli struggled to grind into gear, and Samu should have settled the contest when he broke free on the counter.
Jakub Kiwior did the job instead, as the Partenopei were undone from a corner once again 10 minutes from time.
And things went from bad to worse for the Neapolitans when Rafa Marin was shown a straight red card for hauling Samu down in the box in the 89th minute, only for the striker to dust himself off and score the resulting spot-kick.
The result is a timely lifeline for Porto, marking their first victory in the last seven meetings with Italian opposition (D3, L3).
Napoli are now winless in their previous eight UCL away games (D1, L7), and they have slipped out of the play-off places, as well as being leapfrogged by the Portuguese side.
Flashscore Man of the Match: Jan Bednarek (Porto)