- Henrikh Mkhitaryan (5', 69')
- Marcus Thuram (38')
- Hakan Calhanoglu (79' Pen)
- Davide Frattesi (90'+3')
- Rafael Leão (57')
Inter, who won their first three matches without conceding a goal, moved two points clear at the top of the standings on 12 points from four games.
Mkhitaryan, Marcus Thuram, Hakan Calhanoglu and Davide Frattesi were all on target for Inter, securing their fifth consecutive win in the Milan derby across all competitions for the first time in history.
"Last year, four derby wins brought us a [Coppa Italia] trophy and allowed us to play in a very important [Champions League] final," coach Simone Inzaghi told a press conference.
"[Today's victory] gives us first place, but the championship is still very long."
Mkhitaryan struck from close range to put Inter in front in the fifth minute and new signing Thuram doubled the advantage before the break with a fine shot into the top corner for his second Serie A goal.
Inter allowed Stefano Pioli's side control of possession but were far more ruthless and Mkhitaryan made it 3-1 in the 69th minute before midfielder Calhanoglu added the fourth from a penalty awarded for Theo Hernández's foul on Lautaro Martínez.
Substitute Frattesi completed the rout in stoppage time when he was fed by Mkhitaryan and the 23-year-old outwitted the goalkeeper to find the back of the net.
"A derby lost like this weighs a lot. I'm really sorry, especially for the fans," Milan defender Simon Kjaer told DAZN.
"Tonight they were smarter than us, we [only] played until 3-1."
- Simone Sozza