Jose Mourinho's team are now fifth in the Serie A table and three points outside the Champions League places.
Milan were under pressure after Napoli had opened up a three-point gap at the top of the table after claiming the spoils in a 1-0 derby victory over Salernitana.
Juve are up to sixth on 15 points, level with Atalanta and Fiorentina, while champions Inter are seven points behind Napoli and city rivals AC Milan in third place.
Napoli have 24 points, two more than AC Milan, after equalling the best start in club history, having also won their first eight games in 2017-18.
Barcelona visit Cadiz in the Spanish league with pressure mounting significantly on manager Ronald Koeman.
PSG's fans are set for their first glimpse of Messi at home after his summer arrival from Barcelona. Messi came close to his first goal when he hit the crossbar against Brugge.
Serie A: AC Milan follow Liverpool lesson with trip to old rivals Juventus; Champions Inter face Bologna
AC Milan bounce straight from one massive game to another on Sunday when they travel to fierce rivals Juventus still reeling from defeat in their first Champions League match since 2014.
UEFA Europa League, Europa Conference League: When and where to watch the matchday 1 games as second and third tier competitions in Europe gets underway.
Serie A: El Shaarawy's last-gasp winner takes Roma to top of league table; Zlatan scores on comeback
Roma lead the Serie A table with three wins and 9 points. AC Milan also have three wins from as many matches.
Chelsea visit Arsenal in a London derby and could hand a debut to Romelu Lukaku.
Italian media put the cost of the loan deal at €1 million, with an option to make the move permanent after one year estimated at €4.5 million.
The Milan derby between Inter and AC Milan will take place on matchday 12 on 7 November with the return leg on 6 February.
The 33-year-old becomes new Portuguese coach Jose Mourinho's first signing in a deal that runs until June 2024 and is worth an initial 11.5 million euros ($13.5 million) plus bonuses, the club said.
Serie A: Lazio boss Maurizio Sarri says city rival Jose Mourinho’s glittery managerial past ‘doesn’t count for anything’
Mourinho will coach Roma while Sarri takes charge of city rivals Lazio, both housed in the same stadium in the Italian capital.
Waving the club's yellow and red scarf, Mourinho briefly addressed the crowd before being driven away to the club's Trigoria training centre for the first time.
Serie A: 'Fans, I'm coming,' Jose Mourinho set to arrive in Italian capital as AS Roma hope to end 20-year drought
Mourinho had only been out of work for 15 days after leaving Tottenham two months ago before his return to Serie A was announced on a three-year deal.
Serie A: Alvaro Morata bags brace as Juventus qualify for Champions League with AC Milan; Napoli miss out
Napoli had to settle for a Europa League spot, finishing fifth, one point behind Juventus, after a 1-1 draw at home against Hellas Verona.
Stefano Pioli's side could have sealed a return to elite European football for the first time since the 2013-2014 season with a win over the Sardinians.
Manchester United players have to face the prospect of four Premier League fixtures in 10 days after Edinson Cavani's brace staved off a valiant attempt at a comeback from AS Roma
Mourinho signed a three-year contract on Tuesday and will take charge of the Serie A club after Fonseca sees out the current campaign.