MISSED the match? Catch up via beIN SPORTS CONNECT | 2-WEEK free trial
Martinez netted either side of the interval in the Lombardy derby at Giovanni Zini Stadium.
With a sharp finish having cancelled out David Okereke's sensational opener in the first half, Martinez lashed home from inside the area in the 65th minute.
The victory took Inter to 40 points and, temporarily at least, second place on the table, although runaway leader Napoli holds a 10-point lead.
Inter's bright start failed to produce a true chance, and it was stunned by an incredible 11th-minute opener when Okereke curled a sublime strike in off the underside of the crossbar.
Yet Cremonese's lead lasted just 10 minutes, with Martinez reacting sharply to turn home after Marco Carnesecchi parried Edin Dzeko's volley.
Andre Onana's save prevented Marco Benassi's close-range flick restoring Cremonese's lead, before Martinez drilled just wide at the other end.
Martinez snatched at another chance before the break, sending a tame rebound at Carnesecchi after Federico Dimarco's shot.
Carnesecchi was called into action again after the restart to ensure Dimarco's cross did not find its way in, but Inter kept the pressure on and was rewarded with 25 minutes remaining, Dzeko slipping Martinez in, and the Argentinian hammered the ball beyond Carnesecchi.
Martinez made way for Joaquin Correa soon after with his work done, but Matteo Darmian's last-ditch block from Cristian Buonaiuto's scuffed attempt was required to ensure Inter headed home with the three points.