The Colombia striker, reportedly a target for Chelsea, took his goal tally for the season to 13 in all competitions as the Portuguese champions got back on track.
Porto coach Paulo Fonseca has come under pressure due to their poor form of late and the 40-year-old warned they could ill afford to slip up once again following a 1-0 defeat at Academica last weekend.
Fonseca's side produced the response he was looking for on Saturday night to move above Sporting Lisbon and Benfica.
Martinez opened the scoring three minutes into the second half when he received the ball in the penalty area and turned sharply before unleashing a shot that was deflected into the net.
The sought-after striker then showed why he is so highly rated by sealing the points 10 minutes from time, when he was on hand to finish after good work from Silvestre Varela.
Earlier on Saturday, Estoril chalked up yet another away victory to move to up to fourth as bottom-of-the-table Pacos Ferreira were consigned to a 3-0 defeat.
Marco Silva's side have now won five of their six league games on the road, while Pacos missed an opportunity to move out of the relegation zone.
Javier Balboa opened the scoring after 11 minutes and further strikes from Joao Pedro Galvao and Bruno Lopes in the final 13 minutes heaped more misery on Pacos.
In the other game on Saturday, Vitoria Guimaraes moved up a place to sixth but they were unable to secure all three points as they were held to a goalless draw at home to struggling Belenenses.
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