That result leaves Inter sitting at the top of Serie A with 12 points from their opening four matches.
AC Milan are third with nine points.
Juventus, who beat Lazio earlier today, are second with 10.
FULL-TIME
Inter Milan 5-1 AC Milan
What a result for Inter.
They have won five Milan Derbies in a row for the first time in the fixture's history and Simone Inzaghi's men continue their perfect start to the Serie A season.
AC Milan fought well at times but ultimately couldn't match their rivals' level.
Post update
Inter Milan 5-1 AC Milan
Inter will record their biggest Serie A home win over AC Milan since a 4-0 win in April 1967.
GOAL Inter Milan 5-1 AC Milan
Davide Frattesi (90+2 mins)
What a way to seal a fantastic performance!
Inter outnumber AC Milan as they break and Mkhitaryan slots through Davide Frattesi, who cooly tucks past Mike Maignan.
Post update
Inter Milan 4-1 AC Milan
Five minutes are added on at the end of the second half.
Post update
Inter Milan 4-1 AC Milan
Despite their lead Inter have had just 39% of the ball in this game. They've been at their best on the break.
SUBSTITUTION
Inter Milan 4-1 AC Milan
Ruben Loftus-Cheek goes off for AC Milan. Yunus Musah takes his place.
Post update
Inter Milan 4-1 AC Milan
AC Milan look dejected now.
Even with a three-goal advantage Inter aren't letting up in their attacking pressure.
SUBSTITUTION
Inter Milan 4-1 AC Milan
Hakan Calhanoglu's evening is over, however, and he is replaced by Kristjan Asllani.
GOAL Inter Milan 4-1 Milan
Hakan Calhanoglu (penalty, 79 mins)
Hakan Calhanoglu rifles home from the spot.
It's surely all over now.
PENALTY
Inter Milan 3-1 AC Milan
Lautaro Martinez is fouled in the box by Theo Hernandez and Inter have a chance to score a fourth!
SUBSTITUTION
Inter Milan 3-1 AC Milan
Now AC Milan look to the bench.
Luka Jovic and Noah Okafor come onto the pitch.
Olivier Giroud and Tijani Reijnders make way.
SUBSTITUTION
Inter Milan 3-1 AC Milan
Inter make another change with Stefan de Vrij replacing Alessandro Bastoni.
Post update
Inter Milan 3-1 AC Milan
Inter are on a roll now and go forward through Carlos Augusto. They are moving at breakneck speed on the transition.
GOAL Inter Milan 3-1 AC Milan
Henrikh Mkhitaryan (69 mins)
Inter restore their two-goal advantage!
Henrikh Mkhitaryan receives the ball on the edge of the box and he rifles home, though his effort took a significant deflection.
It's a long rod back for AC Milan now.
Post update
Inter Milan 2-1 AC Milan
AC Milan are struggling to ignite any sort of comeback since Leao's goal. Inter are well-composed, have dropped deeper once again, and the space just isn't there for AC to pose any threat.
SUBSTITUTION
Inter Milan 2-1 AC Milan
Inter turn to the bench with Nicolo Barella, Feferico Demarco and Marcus Thuram making way for Davide Frattesi, Carlos Augusto and Marko Arnautovic.
YELLOW CARD
Inter Milan 2-1 AC Milan
Theo Hernandez goes into the referee's book after mistiming a tackle on Henrikh Mkhitaryan.
Post update
Inter Milan 2-1 AC Milan
The rain at San Siro is nothing short of torrential and the ball is now skidding across the pitch.
Post update
Inter Milan 2-1 AC Milan
That's the first goal Inter have conceded this season.
Live Reporting
Adam Millington
All times stated are UK
Latest PostPost update
FT: Inter Milan 5-1 AC Milan
That result leaves Inter sitting at the top of Serie A with 12 points from their opening four matches.
AC Milan are third with nine points.
Juventus, who beat Lazio earlier today, are second with 10.
FULL-TIME
Inter Milan 5-1 AC Milan
What a result for Inter.
They have won five Milan Derbies in a row for the first time in the fixture's history and Simone Inzaghi's men continue their perfect start to the Serie A season.
AC Milan fought well at times but ultimately couldn't match their rivals' level.
Post update
Inter Milan 5-1 AC Milan
Inter will record their biggest Serie A home win over AC Milan since a 4-0 win in April 1967.
GOAL Inter Milan 5-1 AC Milan
Davide Frattesi (90+2 mins)
What a way to seal a fantastic performance!
Inter outnumber AC Milan as they break and Mkhitaryan slots through Davide Frattesi, who cooly tucks past Mike Maignan.
Post update
Inter Milan 4-1 AC Milan
Five minutes are added on at the end of the second half.
Post update
Inter Milan 4-1 AC Milan
Despite their lead Inter have had just 39% of the ball in this game. They've been at their best on the break.
SUBSTITUTION
Inter Milan 4-1 AC Milan
Ruben Loftus-Cheek goes off for AC Milan. Yunus Musah takes his place.
Post update
Inter Milan 4-1 AC Milan
AC Milan look dejected now.
Even with a three-goal advantage Inter aren't letting up in their attacking pressure.
SUBSTITUTION
Inter Milan 4-1 AC Milan
Hakan Calhanoglu's evening is over, however, and he is replaced by Kristjan Asllani.
GOAL Inter Milan 4-1 Milan
Hakan Calhanoglu (penalty, 79 mins)
Hakan Calhanoglu rifles home from the spot.
It's surely all over now.
PENALTY
Inter Milan 3-1 AC Milan
Lautaro Martinez is fouled in the box by Theo Hernandez and Inter have a chance to score a fourth!
SUBSTITUTION
Inter Milan 3-1 AC Milan
Now AC Milan look to the bench.
Luka Jovic and Noah Okafor come onto the pitch.
Olivier Giroud and Tijani Reijnders make way.
SUBSTITUTION
Inter Milan 3-1 AC Milan
Inter make another change with Stefan de Vrij replacing Alessandro Bastoni.
Post update
Inter Milan 3-1 AC Milan
Inter are on a roll now and go forward through Carlos Augusto. They are moving at breakneck speed on the transition.
GOAL Inter Milan 3-1 AC Milan
Henrikh Mkhitaryan (69 mins)
Inter restore their two-goal advantage!
Henrikh Mkhitaryan receives the ball on the edge of the box and he rifles home, though his effort took a significant deflection.
It's a long rod back for AC Milan now.
Post update
Inter Milan 2-1 AC Milan
AC Milan are struggling to ignite any sort of comeback since Leao's goal. Inter are well-composed, have dropped deeper once again, and the space just isn't there for AC to pose any threat.
SUBSTITUTION
Inter Milan 2-1 AC Milan
Inter turn to the bench with Nicolo Barella, Feferico Demarco and Marcus Thuram making way for Davide Frattesi, Carlos Augusto and Marko Arnautovic.
YELLOW CARD
Inter Milan 2-1 AC Milan
Theo Hernandez goes into the referee's book after mistiming a tackle on Henrikh Mkhitaryan.
Post update
Inter Milan 2-1 AC Milan
The rain at San Siro is nothing short of torrential and the ball is now skidding across the pitch.
Post update
Inter Milan 2-1 AC Milan
That's the first goal Inter have conceded this season.