Martínez finished second last year with five goals fewer than Osimhen.
The Argentina World Cup winner got his campaign off to the perfect start as he opened his account in the 8th minute, side-footing home a low cross from Denzel Dumfries.
Martínez doubled his tally in the 76th, tapping in at the far post after Marko Arnautović rolled it across the face of goal.
Inter Milan had 15 shots on goal, but only managed to steer three on target.
Monza had slightly more of the ball than Inter and created eight chances in total.
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AAP
