David Okereke got the hosts off to a flying start by putting Cremonese ahead in the 11th minute with a well-placed shot from the edge of the box that beat the Inter keeper and hit the underside of the bar before bouncing in.
The goal sent the home fans into raptures and put the visitors on the back foot.
However, Inter did not let the early setback discourage them, and their persistence paid off 10 minutes later when Martinez was in the right place at the right time inside the box to finish on the rebound after Cremonese keeper Marco Carnesecchi had parried Edin Dzeko's volley.
The equalizer breathed new life into Inter and they continued to push forward in search of the winner.
World cup winner Martinez eventually put the visitors ahead in the 65th minute with his 11th goal in Serie A this season.
Dzeko played him in with a perfectly weighted through ball and Martinez's shot from inside the box took a deflection before looping past the keeper. The goal was the result of a well-coordinated team effort and was the turning point in the match.
Inter, who are now second in the league with 40 points, are 10 points behind leaders Napoli, who have played one game more.
Meanwhile, Cremonese remains at the bottom of the league with only 8 points and still searching for their first win of the season after 20 games.