Martínez scored his first league goal on 25 August from the penalty spot against Vitória de Guimarães in the 80th minute, with Porto winning the game 4–0. Against rivals Sporting CP, he scored a back heel volley in a 2–0 win. In the 2012–13 UEFA Champions League group stage on 24 October, Martínez scored his first goal in European competition thanks to an assist by fellow Colombian James Rodríguez. He added another goal later into the match, which ended in a 3–2 victory for Porto against Dynamo Kyiv.