Karim Benzema's fine run of form continued with a double as Real Madrid won at Celta Vigo to move up to second place in La Liga.
Lautaro Martinez's late winner stretched Inter's winning run to eight games, while Cristiano Ronaldo answered his critics with a perfect hat-trick.
Timothy Weah and Jonathan David both scored as Lille won 3-0 at Bordeaux on Wednesday to stay top of the French league ahead of Lyon and PSG.
Marseille's game against Rennes was postponed hours before kick-off after angry Marseille fans marched to the club's training complex to protest against poor results.
Real Madrid drew level with Atletico Madrid at the top of La Liga with a 2-0 win over Granada, plus all the latest from Serie A and La Liga.
Barcelona's dismal start to the La Liga season continued as a second-half winner from substitute Alvaro Negredo handed Cadiz another major top-flight scalp.
Olivier Giroud's injury-time header against Rennes booked Chelsea's place in the knockout stages of the Champions League.
Team news and stats ahead of Rennes vs Chelsea in the Champions League group stage on Tuesday; kick-off 5.55pm.
Timo Werner scored two penalties as Chelsea made it three wins on the bounce without conceding, easing past 10-man Rennes 3-0.
Lionel Messi became the first player to score in 16 consecutive Champions League seasons as he guided 10-man Barcelona to a 5-1 victory over Ferencvaros.
Sergio Ramos' late penalty helped secure Real Madrid a 3-2 victory at Real Betis, who finished the La Liga match with 10 men, plus all the latest from around Europe.
Chelsea have signed goalkeeper Edouard Mendy from Rennes for £22m on a five-year deal.
Chelsea are close to agreeing a deal to sign goalkeeper Edouard Mendy from French club Rennes.
Chelsea are in talks with Rennes over goalkeeper Edouard Mendy after ending their interest in Lille's Mike Maignan.
Neymar was sent off as PSG moved 13 points clear at the top of Ligue 1 following a dramatic 4-3 win over Bordeaux.
Mauro Icardi rediscovered his scoring touch to help PSG beat Nantes 2-1 in Ligue 1 while Borussia Dortmund and RB Leipzig were knocked out of the DFB-Pokal in Germany.
Erling Haaland continued the remarkable start to his Borussia Dortmund career with two more goals in a 5-1 win over Cologne in the Bundesliga on Friday.
Cristiano Ronaldo scored his first Juventus goal since October to rescue a 2-2 Serie A draw against Sassuolo.
Already-qualified Celtic secured top spot in Europa League Group E as Ligue 1 side Rennes were comfortably beaten 3-1 in Glasgow.
Javier Hernandez scored his first La Liga goal for Sevilla whose 2-0 win over Getafe took them level with second-placed Barcelona.
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