The win extends Inter's lead over Milan to four points atop the Serie A table.
Lautaro Martinez opened the scoring with a close-range header off of Romelu Lukaku's curling cross into the box.
Milan pressed for an equalizer right after the break, forcing Inter 'keeper Samir Handanovic to make two impressive saves in the opening minutes of the second half.
But Inter made life harder for their city rivals shortly after by doubling their lead on an impressive passing sequence that Martinez capped off with his second goal of the contest.
Lukaku put the match to rest in the 66th minute with a powerful curling shot inside the near post. Milan star Zlatan Ibrahimovic applauded the goal after being involved in a heated dispute with Lukaku in the Coppa Italia quarterfinal last month.
The Belgian's Serie A-leading 17th tally marked the fourth straight time he's scored in a Milan derby, a feat that hasn't been achieved in 48 years.
The victory is Inter's fourth consecutive league win, and their second straight against Milan this season. The Nerazzurri haven't won the Scudetto since 2010.