Inter needed the victory to leapfrog Milan and go top of the table, something they had not experienced during the second half of the Serie A season since the Treble campaign of 2009-10.
Romelu Lukaku scored two and created the other for Lautaro Martinez, as although Lazio had more possession, Inter won 3-1 at the Stadio Meazza.
The Belgian scored his 299th and 300th career goal, both of them came in the first half.
He sent Pepe Reina the wrong way to convert a spot-kick before before VAR was for the second Inter goal, which was initially disallowed for offside.
Brozovic’s sliding tackle ricocheted off Manuel Lazzari’s shin and into the path of Lukaku to score. It was not an intentional pass. However, when Brozovic made the initial touch, Lukaku was level and therefore Lazzari’s contribution was irrelevant.
Inter are now the Serie A table leaders with 50 points in 22 games. Milan are just one point off the Nerazzurri with the two sides meeting in the Derby della Madonnina next week.