Manchester City humbled their neighbours United by beating them 6-1 and Levante still lead in Spain where European champions Barcelona were held to a 0-0 draw by Sevilla.
Manchester City crushed Manchester United 6-1 at Old Trafford and Chelsea had two players sent off and lost 1-0 at Queens Park Rangers on a remarkable day in the Premier League.
Mario Balotelli and Edin Dzeko each scored twice and Sergio Aguero and David Silva added the others as City ended United's 18-month home unbeaten run and moved five points clear of the champions at the top of the table.
Chelsea had Jose Bosingwa and Didier Drogba sent off in the first half at Loftus Road where a Heidar Helguson penalty secured the points and a first home win of the season for Rangers.
Surprise packages Levante continued their remarkable early-season run when the tiny Valencia-based club stunned Villarreal 3-0 to move a point clear of Real Madrid at the top.
Jose Mourinho's Real were the overnight leaders after they thrashed Malaga 4-0 on Saturday thanks to a Cristiano Ronaldo hat-trick.
Champions Barcelona, bidding for a fourth consecutive title, slipped to third after they were held to a 0-0 draw at home to Sevilla, in fourth.
The match at the Nou Camp ended in acrimony after Barca were awarded a stoppage-time penalty and a mass brawl erupted which led to the dismissal of Sevilla striker Frederic Kanoute.
Goalkeeper Javi Varas saved Lionel Messi's spot kick before the visitors had defender Fernando Navarro sent off for a wild tackle on Pedro.
Leaders Bayern Munich conceded their first league goal for more than eight games and had Jerome Boateng sent off for fighting before the half hour as they lost 2-1 at Hanover 96.
Mohammed Abdellaoue's 23rd minute penalty for Hanover was the first goal that Manuel Neuer had conceded in 761 minutes of play in the Bundesliga, the last being on the opening day against Borussia Moenchengladbach.
Bayern remained on 22 points from 10 games and their lead was cut to three points by defending champions Borussia Dortmund, who thrashed Cologne 5-0 with Robert Lewandowski scoring twice.
Schalke 04, who beat Bayer Leverkusen 1-0 after Jefferson Farfan ran 60 metres to score the winner, and Hanover 96 are a further point behind.
Kevin-Prince Boateng came on at halftime with AC Milan losing 3-0 at Lecce and scored a hat-trick within 18 minutes to fire them to an astonishing 4-3 win. Colombian Mario Yepes headed the winner to leave Milan with 11 points from seven games.
Udinese went top with 15 points thanks to a 3-0 win over Novara with Antonio di Natale, last season's topscorer, scoring twice.
Argentine teenager Erik Lamela scored after seven minutes of his Serie A debut to give AS Roma a 1-0 win over Palermo and Inter Milan beat Chievo by the same score for only their second league win of the season.
Leaders Paris St Germain needed a brace from Nene to beat promoted Dijon 2-0 and flying Montpellier stayed three points behind after a 3-1 victory at Caen.
Lille, inconsistent so far in the defence of their title, won the weekend's big French clash against Olympique Lyon 3-1 with Joe Cole rounding off the comeback victory in the north east.
Olympique Marseille stopped the rot with a 2-0 home win over bottom side Ajaccio but tensions remain between the club, fans and coach Didier Deschamps.
Rivals Porto and Benfica both won and retained their joint-lead in the Portuguese Premier League, on 20 points after eight matches.
Stocky Brazilian striker Walter scored one and set up another as Porto crushed Nacional 5-0 at home. Walter backheeled the ball for Belgium's Steven Defour's opener and then tapped in the 2-0 himself. Right-back Cristian Sapunaru scored the third before Brazilians Kleber and Hulk added one each.
Paraguay's Oscar Cardozo headed in the decider in Benfica's 1-0 win at Beira Mar. Cardozo scored close to the half-time whistle, arriving first to a kick clearance that Beira Mar keeper Rui Rego embarrassingly fumbled.