Cristiano Ronaldo scored five goals on a record-setting Saturday for Real Madrid, while Manchester City made it five straight wins to start its campaign to reclaim the Premier League title.
City needed a 90th-minute winner to down Crystal Palace 1-0, while defending champion Chelsea slumped to a 3-1 defeat at Everton that sealed its worst start in the EPL.
Ronaldo recorded his second career five-goal game to lead Madrid's 6-0 rout at Espanyol, taking his tally to 231 goals and eclipsing Raul Gonzalez's mark of 228 goals. He reached the milestone in 203 matches, compared to Raul's 550.
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Also in Spain, Lionel Messi went on as a substitute to give Barcelona a 2-1 win at potential title rival Atletico Madrid.
Here is a look at Europe's major leagues on Saturday:
City kept winning thanks to 18-year-old Kelechi Iheanacho coming off the bench in the 89th and poking the ball into the Palace net a minute later.
Another teenager, 19-year-old Anthony Martial, scored on his debut in Manchester United's 3-1 win over Liverpool, and Arsenal comfortably beat Stoke 2-0 on goals by Theo Walcott and Olivier Giroud.
Chelsea was torn apart by hat-trick scorer Steven Naismith, who went on as a ninth-minute substitute for the injured Muhamed Besic and struck twice before Nemanja Matic scored Chelsea' goal. Naismith sealed the win in the 82nd.
Chelsea was 11 points behind City, which was also reveling in a five-point lead over United and Arsenal.
There was plenty for United fans to celebrate at Old Trafford, with David De Gea making his first appearance of the season in goal after signing a new contract.
Daley Blind and Ander Herrera had United up 2-0 when Christian Benteke pulled one back with an overhead kick in the 84th. Martial then weaved through the Liverpool defense to seal the result.
Watford edged Swansea 1-0 despite being reduced to 10 men. Norwich beat Bournemouth 3-1, and West Brom drew 0-0 at home to Southampton.
Held scoreless in the first two rounds of the season, Ronaldo exploded against Espanyol and had a hat trick by the 20th minute, scoring from passes by Luka Modric and Gareth Bale in between a penalty kick earned by the Welshman.
Ronaldo passed for Karim Benzema to make it 4-0 before halftime, and he scored twice more to move into fourth place on the Spanish league all-time scoring list.
Messi holds the record, which he increased to 286 goals after he again proved decisive at Atletico.
Fernando Torres put Atletico ahead in the 51st minute, only for Neymar to equalize from a free kick four minutes later.
Messi was on the bench following the recent birth of his second son. But he went on for the final half hour and immediately changed the match, scoring the 77th-minute winner from Luis Suarez's pass.
Barcelona sat at the top of the standings with nine points after the defending champion's third win in as many rounds. Madrid was two points behind, and Atletico three behind.
Paco Alcacer headed in Valencia's injury-time winner for 1-0 at Sporting Gijon, while promoted Real Betis edged Real Sociedad 1-0.
Thomas Mueller scored a last-minute penalty for Bayern Munich to beat Augsburg 2-1, and Borussia Dortmund maintained its perfect Bundesliga start by defeating Hannover 4-2.
Alexander Esswein struck for Augsburg two minutes before the break, but Robert Lewandowski equalized in the 77th, and Mueller made no mistake from the spot after Markus Feulner was adjudged to have fouled Douglas Costa.
Hannover defender Felipe scored an own goal and gave away two penalties in a game to forget for the Brazilian.
Pierre-Emerick Aubameyang scored both penalties for Dortmund, with Henrikh Mkhitaryan adding a fine strike, and Felipe doing the rest. Artur Sobiech scored twice for Hannover.
Alexander Meier marked his return from a knee operation with a hat trick as he led Eintracht Frankfurt to a 6-2 rout of Cologne.
Promoted Darmstadt upset Bayer Leverkusen 1-0, Ingolstadt and Wolfsburg drew 0-0, while Hertha Berlin defeated Stuttgart 2-1.
Juventus picked up its first point in the Serie A as a late penalty helped the four-time defending champion rescue a 1-1 draw against surprise front-runner Chievo Verona.
Paulo Dybala converted the spot kick, called after Juan Cuadrado was tripped by Chievo defender Bostjan Cesar.
Perparim Hetemaj got Chievo on the board after just five minutes.
Chievo lost its 100 percent record but remained on top, above Roma on goal difference.
Roma beat local rival Frosinone 2-0, while 10-man Fiorentina topped Genoa 1-0.
Fiorentina's Giuseppe Rossi made his first start in 482 days as he returned from another knee injury.
Lyon missed the chance to move into second place in the French league after drawing 0-0 against Lille.
Reims battled back from two goals down to draw 2-2 at Toulouse, while striker Nolan Roux scored his first goal for his new Saint-Etienne club in a 2-1 win at last-place Montpellier.
Caen secured a 3-1 win at Troyes. Guingamp won 1-0 at Nice, and Lorient beat newly promoted Angers 3-1 on its plastic field.