Barcelona lost for the second straight La Liga game in a 1-0 home reverse against Celta Vigo but there was no such trouble for Manchester City, who beat 10-man Manchester United 1-0 thanks to Sergio Aguero.
Ten-man United beaten in Van Gaal's first Manchester derby
Chelsea and Manchester City earned narrow victories in local derbies but surprise packages Southampton continue to split them at the top of the Premier League.
They won 1-0 at Hull City on Saturday to remain within four points of Chelsea, who beat Queens Park Rangers 2-1.
City are two points further back having beaten Manchester United 1-0 after Chris Smalling was sent off.
Arsenal moved ahead of London rivals West Ham United into the fourth Champions League place with a 3-0 home win over Burnley, who remain bottom without a win after 10 games.
Barca lose at home
Barcelona followed up last weekend's 3-1 defeat at Real Madrid with another loss, squandering a host of chances to go down 1-0 at home to Celta Vigo and hand the lead in La Liga to their arch rivals.
Barca forward Neymar hit the crossbar twice and team mate Lionel Messi, who remains one goal short of La Liga's scoring record of 251, did likewise but hesitation in the defence let in Celta's Joaquin Larrivey to score 10 minutes after halftime.
Real take over at the top on 24 points from 10 matches thanks to a 4-0 win at Granada with James Rodriguez striking twice, including a superb volley, and the prolific Cristiano Ronaldo scoring his 17th goal in nine La Liga games this season.
Champions Atletico Madrid, 4-2 winners at home to Cordoba, are level on 23 points with Valencia who won 3-1 at Villarreal with Barca a point further back.
Leaders Bayern Munich win
Arjen Robben's late penalty gave titleholders and leaders Bayern Munich a 2-1 home win over Borussia Dortmund which kept them four points clear at the top and sent their bitter rivals into the relegation zone.
Marco Reus gave Dortmund a first-half lead but Robert Lewandowski levelled against his old club in the 72nd minute and Robben stroked home the winner in the 85th minute after a foul on Franck Ribery.
Bayern have 24 points from 10 games, four clear of VfL Wolfsburg, who hammered VfB Stuttgart 4-0 away, and Borussia Moenchengladbach, 3-1 winners over previously unbeaten Hoffenheim.
Dortmund's defeat, their fifth in a row in the league, sent them down to 17th place in the 18-team table.
Juventus on top
Juventus went three points clear at the top of Serie A with a 2-0 win at promoted Empoli.
Andrea Pirlo put Juventus ahead with a trademark free kick, the playmaker's first goal of the season, just after the hour and Alvaro Morata scored the second.
The win lifted the champions to 25 points from 10 games, three more than AS Roma who lost 2-0 at Napoli to an early goal from Gonzalo Higuain and a late strike from Jose Callejon.
Sampdoria (19 points) moved into third place with a 3-1 win over Fiorentina and Napoli are one point behind.
Olympique de Marseille lead
Olympique de Marseille retained their four-point lead at the top of the Ligue 1 standings with a 2-1 home win against strugglers RC Lens.
Florian Thauvin scored one and set up another to put OM on 28 points from 12 games while PSG also won 2-1, at Lorient, to stay in the hunt.
Olympique Lyonnais are third a further point back thanks to a 3-1 win at Nice, their fourth league victory in a row.
Monaco are seventh on 18 points after squandering two points in a 1-1 home draw against Stade de Reims.
