Gennaro Gattuso's side stayed unbeaten and won for the fifth time in six matches. Nuno Tavares scored in the third minute, and Gustav Isaksen doubled the lead midway through the first half. Monza lost Lorenzo Lucchesi to a red card in the 35th minute for hauling down Tijjani Noslin as he broke through on goal.
The 16th-placed visitors still rattled Lazio after the break. They pulled a goal back and came close to equalising before Lazio scored a third in the closing stages. Inter had reached 16 points a day earlier with a 3-0 win over Parma at San Siro.
Roma could not keep up. They drew 0-0 at Como, the first goalless draw of the Italian season, after league top scorer Donyell Malen got a red card for a dangerous tackle early in the second half. That left Roma two points behind the leaders. "We played two-thirds of the match a man down, that is the disappointing thing," coach Gian Piero Gasperini told DAZN.
Elsewhere, Bologna beat Lecce 2-1 for their first win of the season.