The Ukrainians threatened to ruin Porto's day after coming from behind twice to level the match but could not prevent the Portuguese side from scoring the winner with 12 minutes remaining.
Silvestre Varela put Porto ahead after 15 minutes when he received the ball in the box from Argentine playmaker Lucho Gonzalez, gently cushioned it and then blasted it straight into the top right corner.
The Ukrainians replied swiftly and five minutes later Oleh Gusyev headed in an inswinging corner with Porto keeper Helton slow to react.
The home side went back on top 10 minutes before half-time through Martinez but in the second half were caught napping by the visitors and Nigerian Ideye Brown levelled again.
Martinez crowned his man-of-the match performance with a tap-in after 78 minutes, giving Porto a maximum nine points from three games.
The Portuguese club, in the Champions League group stage for the 17th time, put their experience to use as they kept calm to seal the win.
"Our first half was quality but although in the second we were not as strong, we achieved our goal," Porto coach Vitor Pereira said. "We grabbed nine points from the first three matches and in the Champions League, it's not any team that does that".
Kiev will take little heart from becoming the first team to score against Porto at the Dragao stadium this season in all competitions.
Paris Saint-Germain are second in the group with six points after a 2-0 win at Dinamo Zagreb. Kiev are third on three points while Zagreb are on zero.
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