If Villarreal coach Unai Emery was unhappy at the space his side left Barca in the opening goal, he will have been furious as Fati doubled his tally just four minutes later.
The 12-time champion also improved his record at Roland Garros to 95-2 with this win.
While both Bayern Munich and Borussia Dortmund suffered disappointing league defeats before crossing swords, the clubs' challenges couldn't be more different.
Also on Tuesday, men's singles seventh seed Matteo Berrettini of Italy cruised to a 6-3, 6-1, 6-3 victory over Canadian Vasek Pospisil.
Libertad are third, level on points with Caracas FC, but with an inferior goal difference.
The 64-year-old, who began his managerial career as a teenager in 1975, had previous spells as Botafogo boss in 1986, 1995, 1998 and 2001.
Attracting around 300 swimmers, the 2020 championships are being held from September 26 to October 2 in Qingdao.
According to the schedule, Guoan will continue to be in the Suzhou division and compete with seven other clubs for the CSL championship this year. Its first opponent is Shandong Luneng, who ranked third in the Dalian division in the first stage. As the second phase of the CSL adopts a two-round knockout system, the two sides will start their first fight on October 17.
Lautaro's scorcher before the interval wiped out Christian Kouame's opener, and the Argentinian then forced Federico Ceccherini into scoring an own goal seven minutes after the break, helping the Nerazzurri turn around the game.
Thiago joined Liverpool from Bayern Munich earlier in September and although he made his debut against Chelsea eight days ago, he missed Monday night's 3-1 win at home to Arsenal.
Seventh seed Petra Kvitova of the Czech Republic is also through after she overcame Jasmine Paolini of Italy 6-3, 6-3.