The first half in Felgueiras was an end-to-end battle as both sides enjoyed good spells, but Porto wasted several chances to take the lead.
Pacos, who entered the game on the back of four successive losses in all competitions to start their season, were hopeful of winning a point as the match entered the final 15 minutes.
But Colombian forward Jackson Martinez, who failed to score from numerous attempts earlier in the match, eventually netted his third league goal of the season.
Martinez – who has scored in every Primeira Liga fixture this season – rose between two defenders to head in Juan Quintero's corner in the 77th minute.
Sporting Braga lost their own perfect record, as they slumped to a 1-0 defeat at Gil Vicente, who finished the match with nine men.
In a fiery match that saw 10 bookings, Brazilian Luan scored the game's only goal with 23 minutes to play.
Defenders Danielson and Halisson were both sent off for the winners, but they kept their more-fancied opponents at bay in the dying stages.
Other matches on Sunday saw Nacional win 3-2 at Belenenses thanks to a double from Mateus, as the losers – who were reduced to 10 men when goalkeeper Matthew Jones was sent off in the 10th minute – fell to their third defeat in a row.
Maritimo and Olhanense were also in action and drew 1-1, while Arouca edged Rio Ave 1-0.
