Although Monza managed to avoid defeat in this fixture last season, they were immediately up against it tonight as the hosts only needed seven minutes to find the opener.
Denzel Dumfries rampaged down the right flank before a driven cross was cleverly tucked home by captain Martinez.
Despite that early setback, the visitors continued to battle, with their best opportunity falling to Andrea Colpani, but the attacker opted to shoot rather than slot in Gianluca Caprari who was better placed inside the box.
Spurred on by the fervent home support, Inter looked increasingly dangerous down both flanks with Dumfries and Federico Dimarco causing chaos on the overlap, but a mixture of solid defending from the away side and poor decision-making ensured the score remained 1-0 going into half-time.
The interval appeared to break Inter’s momentum and it was the visitors who looked the more threatening after the restart, but two dangerous balls into the box were dealt with brilliantly by the home defence as they started to re-establish their dominance.
Although Monza were struggling to create a chance of note, they were hanging tough and the Nerazzurri needed a knockout blow to be sure of the points.
Marko Arnautovic, making his second debut at the club after a wasted spell earlier in his career, made up for lost time as he twisted his defender inside-out before firing a ball towards the far post which was bundled home by Martinez for his second of the evening.
That goal provided a much-needed cushion for Inter, who coasted through the closing exchanges to secure a well-deserved opening-day triumph.
Despite the defeat, Monza can take away plenty of positives from a spirited performance, as they look to build on last season's impressive 11th-placed finish.
Flashscore Man of the Match: Lautaro Martinez (Inter)
In Serie A's other late fixture:
Fiorentina ran riot in the first half away at promoted Genoa, rushing into a three-goal lead before adding a fourth after the break. Genoa pulled one back but it finished 4-1, emphatically in favour of the visitors.
