Ismael Bennacer joins the Milan club from fellow Serie A side Empoli on a five-year contract.
19-year-old Moise Kean came on as a substitute in Turin and three minutes later scored his third league goal of the season after his double against Udinese earlier this month.
The coach joined Roma until the end of the season after Eusebio Di Francesco was sacked.
Inter, now 9 points behind Napoli in 3rd, are just 2 points ahead of city rivals AC Milan who remain 4th after a 3-0 win over Empoli.
The 23-year-old Polish striker joined Milan from Genoa last month and has now scored seven goals in six matches.
Dries Mertens' hattrick led Napoli to a 5-1 win over Empoli.
When Napoli and Empoli face off in a Serie A match, both teams will probably exhibit playing characteristics instilled by former coach Maurizio Sarri.
Ronaldo completed a much more successful week for Juve.
After beating Manchester United in the Champions League, Juventus, spearheaded by Cristiano Ronaldo, will be eager to continue their good form against Empoli.
Steven Nzonzi and Edin Džeko's goals gave Roma a 2-0 win over Empoli.