Cristiano Ronaldo rewrote the record books with another two goals in Real Madrid's latest big victory in the Spanish league.
Southampton crushed Sunderland 8-0 in England while Manchester City's Sergio Aguero scored four goals and Premier League leader Chelsea escaped with a gritty victory.
A look at Europe's top leagues Saturday:
Cristiano Ronaldo netted his 14th and 15th goals to set a record scoring start in a Spanish league season as Real Madrid eased to a 5-0 win at Levante.
Ronaldo scored on a penalty kick in the 13th minute before adding another goal in the 61st, increasing his league-leading tally to 15 goals in eight rounds despite missing one game because of injury. The Portugal forward has scored more than twice as many goals as Neymar, who is second on the scoring list.
The previous best start was by Oviedo's Esteban Echevarria — 14 goals through eight rounds to start the 1943-44 season.
Javier Hernandez, James Rodriguez and Francisco "Isco" Alarcon also scored to rout the overmatched hosts.
Madrid rose to a provisional second place, one point behind Barcelona before it hosts Eibar later when Lionel Messi will also take a shot at the record books. He needs two goals to equal the league's all-time scorer — Athletic Bilbao's Telmo Zarra, who scored 251 goals in 271 games from 1940-55.
Manuel "Nolito" Agudo scored in the 73rd to give Celta Vigo a 1-1 draw at Athletic Bilbao, keeping the Basque club with one win in 10 matches in all competitions not counting its elimination of Napoli from the Champions League playoffs.
Southampton trounced Sunderland 8-0 in one of the biggest wins in the Premier League's 22-year history. His performance overshadowed Sergio Aguero's four-goal haul in Manchester City's latest thrashing of Tottenham.
Chelsea preserved its five-point lead — and its unbeaten start to the campaign — by beating Crystal Palace 2-1 thanks to a free kick from Oscar and a great goal finished off by Cesc Fabregas.
For second-placed Man City, Aguero had two goals in each half. He made two penalty kicks and also missed on in the 4-1 win over 10-man Spurs. The champions have now scored 15 goals in three straight wins over Tottenham.
Southampton stayed a point behind in third after scoring five times in the final 27 minutes against imploding Sunderland, narrowly missing out on equaling the record margin of victory in the Premier League held by Manchester United from its 9-0 win over Ipswich in 1995.
"I'm still a little bit in shock," Southampton manager Ronald Koeman said. "Sometimes football is strange."
Danny Welbeck's stoppage-time strike secured injury-hit Arsenal a 2-2 draw at home with Hull, while goals by Phil Jagielka, Romelu Lukaku and Seamus Coleman earned Everton a 3-0 win over Aston Villa with Ross Barkley making an impressive return from injury for the Toffees.
West Ham's surprising start continued with a 3-1 win at Burnley, lifting the London team provisionally into fourth place.
Newcastle eased some pressure on manager Alan Pardew by beating Leicester 1-0 in a match whose kickoff was delayed an hour after part of a new big screen was dislodged by wind at St. James' Park.
Roma cruised to a 3-0 victory over Chievo Verona in Serie A, a lift before its Champions League match against Bayern Munich on Tuesday.
Roma got off to a quick start when Mattia Destro headed in a corner with less than five minutes gone. The home team made it 2-0 in the 25th minute. Adem Ljajic latched onto a long ball from Francesco Totti and burst into the box before firing into the far corner.
Totti sealed the match shortly after 30 minutes with a penalty kick after Daniel De Rossi had been hauled down by Dario Dainelli.
Roma, for now, is tied for first with Juventus, which visits Sassuolo later.
Borussia Dortmund slumped to its fourth defeat in five Bundesliga games with a 2-1 loss at Cologne. League leader Bayern Munich routed helpless Werder Bremen 6-0.
Despite the return of key players from injury, Dortmund was unable to end its five-game run without a win. The club is two points off the relegation zone after eight matches. It will be just one point if Hamburger SV wins Sunday.
Kevin Vogt put Cologne ahead five minutes before the break. Ciro Immobile tied it three minutes into the second half but a mistake by goalkeeper Roman Weidenfeller allowed Simon Zoller to score the winner in the 74th.
Bayern captain Philipp Lahm and Mario Goetze both scored twice in a rout in which top striker Robert Lewandowski remained on the bench.
Elsewhere, Stuttgart fought from three goals down to draw 3-3 with Bayer Leverkusen; Max Kruse scored twice as Borussia Moenchengladbach defeated Hannover 3-0 on the road; Mainz beat Augsburg 2-1; and Wolfsburg won 2-1 at Freiburg on two goals from former Freiburg midfielder Daniel Caligiuri.
Schalke was hosting Hertha Berlin in the late game with new coach Roberto di Matteo in charge.
Midfielder Fabien Lemoine scored a late winner to help Saint-Etienne win 1-0 at Lorient and temporarily move into fourth place.
Ricky van Wolfswinkel had a shot in each half saved by goalkeeper Benjamin Lecomte, and winger Max-Alain Gradel failed to connect from Kevin Monnet-Paquet's cross in the 78th minute when left unmarked. But Lemoine atoned for those misses in the 87th with a low shot from outside the penalty area.
Lille can move back above Saint-Etienne if it beats last-placed Giungamp later Saturday.
On Friday, two-time defending champion Paris Saint-Germain topped Lens 3-1.