Real Madrid suffered a shock 1-0 home loss to promoted Cadiz while Barcelona were beaten by the same scoreline at Getafe, who moved into second place in LaLiga.
Real head coach Zinedine Zidane offered no excuses as the reigning champions slumped to a first ever loss against Cadiz.
Anthony Lozano's first-half goal proved enough for an unlikely win for the newcomers, who held off a second-half onslaught at the Estadio Alfredo Di Stefano with Karim Benzema's late effort crashing off the crossbar.
Barcelona, though, failed to capitalise as a penalty from Jaime Mata after 56 minutes settled matters at the Coliseum Alfonso Perez.
Lionel Messi had struck a post during the first half, but it was a frustrating evening for the Catalans as Getafe, who also hit the woodwork during the closing stages, went level on points with leaders Madrid.
Barca's first defeat of the season under head coach Ronald Koeman leaves them ninth in the table, three points adrift, but still with a game in hand.
Luis Suarez's early goal set Atletico Madrid on their way to a 2-0 win at Celta Vigo, with substitute Yannick Carrasco adding a second in stoppage time.
Granada beat Sevilla 1-0 with a late goal from Yangel Herrera after the visitors had seen midfielder Joan Jordan Moreno sent off just before half-time.
Zlatan Ibrahimovic scored twice in the first half – one from a rebound off his saved penalty – as Serie A leaders AC Milan beat Inter 2-1 to win the Derby della Madonnina.
Ibrahimovic, fit again following a positive Covid-19 test, put the Rossoneri ahead after 13 minutes when he tucked home at the second attempt after his spot-kick had been kept out by Samir Handanovic.
It was soon 2-0 following a swift counter, Ibrahimovic slotting in a left-wing cross from Rafael Leao.
Inter pulled a goal back from Romelu Lukaku after 29 minutes, but it was AC Milan who took the spoils to maintain their perfect start.
RB Leipzig kept themselves a point clear at the top of the Bundesliga with a 2-0 win at Bavarian rivals Augsburg.
Defender Angelino headed the visitors in front on the stroke of half-time, with substitute Yussuf Poulsen volleying in a second soon after coming on after 66 minutes.
Bayern Munich won 4-1 at Arminia Bielefeld, where Thomas Muller and Robert Lewandowski both scored twice and midfielder Corentin Tolisso was sent off late on.
The visitors had to use changing rooms in a nearby school before the game because of the strict Covid-19 regulations.
Borussia Dortmund are also on nine points from four matches after a late goal from Marco Reus secured a 1-0 win at Hoffenheim.
Stuttgart won 2-0 at Hertha Berlin to sit fourth, while struggling Mainz lost 1-0 at home against Bayer Leverkusen.
Saturday's late kick-off saw Wolfsburg draw 1-1 at Borussia Monchengladbach with a late goal from Wout Weghorst, while it was also 1-1 between Freiburg and Werder Bremen.
In France, Marseille saw off Bordeaux 3-1 to record a first Ligue 1 win in five matches.
Florian Thauvin fired the hosts into an early lead after only five minutes, with Jordan Amavi also on target in the second half.
An own goal from Pablo wrapped things up ahead of a late consolation from Bordeaux substitute Josh Maja.
Earlier, Lorient came from behind to win 3-1 at struggling Reims, who had midfielder Moreto Cassama and substitute Anastasios Donis sent off during the closing stages.
