AC Milan won for only the second time in five Serie A matches when it beat Genoa 1-0.
The Bianconeri's 100 per cent record came to an end.
Both teams want to finish in top four and qualify for Champions League next term.
Inter were looking to bounce back after their Serie A 1-1 draw to Cagliari.
Juventus came into the game on a real roll, having won six on the bounce.