The visitors came out aggressively, with Hakan Calhanoglu leading the charge. They dominated possession and made it difficult for Cagliari to leave their own half. It was no surprise when Martinez headed home from Alessandro Bastoni's cross in the ninth minute.
Cagliari struggled to respond, with Sebastiano Esposito missing a presentable free-kick and his teammates struggling to win the ball back from Inter. When they did gain possession, mistakes from Michael Folorunsho and Alessandro Deiola cost them valuable time.
Despite some urgency from Cagliari at the start of the second half, Inter continued to create the better chances. Calhanoglu's shot hit the post, and Marcus Thuram's effort was saved by the goalkeeper.
Cagliari's attempts to get back into the game were thwarted by Inter's superior play. A late header from Folorunsho came back off the woodwork, but it was Inter who scored the decisive goal when Francesco Pio Esposito fired in his first Serie A goal.
Henrikh Mkhitaryan orchestrated the win, which marks Inter's fourth victory in 11 away games and their 14th win in 16 league head-to-heads against Cagliari.