Madrid: Jude Bellingham starred as Real Madrid made it three wins in three games under José Mourinho in La Liga, while former coach Xabi Alonso also enjoyed another victory with Chelsea.
Bellingham scored one goal and created another as Kylian Mbappé and substitute Arda Güler also found the net in Madrid's 4-0 home win over promoted Malaga, who are back in La Liga after eight years.
Chelsea emerged with a 4-3 win over Brighton in the Premier League, while Bruno Fernandes scored a hat-trick as Manchester United bounced back from an early setback against Ipswich to win 5-2.
Bellingham unstoppable in Spain
Bellingham, who scored Madrid's first goal of the season, opened the scoring again on Sunday after surging past a couple of Malaga defenders and shooting past goalkeeper Alfonso Herrero from a narrow angle. Some fans inside the stadium responded by singing the Beatles hit 'Hey Jude'.
He then forced the ball over the line shortly afterwards, heading in the rebound from Mbappé's attempt. Malaga defender Carlos Puga's desperate attempt to clear the ball struck Herrero's back before going into the net.
Mbappé effectively sealed the result inside the first half-hour when he volleyed Trent Alexander-Arnold's cross into the net. Alexander-Arnold made his first start at right-back after new signing Denzel Dumfries had started the opening two games.
Bellingham struck the post and went close again in the second half before Güler completed the scoring following unselfish play from Vinícius Júnior.
Left-back Marc Cucurella impressed on his first start since joining Madrid from Chelsea.
Elsewhere, Pierre-Emerick Aubameyang scored again as Deportivo La Coruña defeated Valencia 3-1 for its first win since returning to the top division.
Athletic Bilbao won 2-0 against Celta Vigo, who suffered their second straight home defeat. Celta are yet to win a La Liga game this season after opening with a 0-0 draw at Valencia.
Barcelona will play a depleted Rayo Vallecano side on Monday.
A scare for United in Premier League
When Ipswich scored first, Manchester United fans may have feared the worst after the shock loss to Hull, another promoted team, the previous week.
But Fernandes, the Premier League's player of the year last season, responded with a clinically taken hat-trick to inspire United's comeback win at Old Trafford.
Alonso watched as his Chelsea team prevailed 4-3 over Brighton in a wild Premier League encounter.
Cole Palmer starred for Chelsea, but Alonso will have concerns about the team's defence as well as an injury to key midfielder Moisés Caicedo.
Argentina's Emiliano Martínez played in goal for Chelsea after the club announced his transfer from Aston Villa just hours before the match.
Schalke's Bundesliga return
After three seasons away, Schalke endured a difficult return to the German top flight as it slumped to a 3-0 loss at Augsburg.
Schalke's defence looked shaky and defender Ron Schallenberg was sent off for bringing down Michael Gregoritsch with half an hour remaining. Gregoritsch had opened the scoring and was on course to add another before the impressive Anton Kade and Rodrigo Ribeiro completed the scoring.
Freiburg routed Werder Bremen 4-1 in the early match.
Defending champions Bayern Munich opened their league campaign with a 5-1 rout of Stuttgart on Friday.
Como win duel with Napoli in Serie A
Como got the better of Napoli in a Serie A duel between Champions League participants, securing a 2-1 victory in Naples.
The visitors capitalised on defensive mistakes, with Tassos Douvikas and Martin Baturina scoring either side of Rasmus Højlund's brief response for Napoli in the first half.
Defending champions Inter Milan needed another long-range strike from Hakan Çalhanoğlu to beat Cagliari 1-0 away. Çalhanoğlu scored a similar goal in the opening 4-1 win over Monza.
Paris fires Monaco to success in France
German youth international Paris Brunner scored twice to lead Monaco to a 2-0 home win over Marseille.
Brunner opened the scoring early with a header before sealing the result with a brilliant individual goal early in the second half. He eluded one defender, then another, before sweeping the ball into the net.
The result left Monaco as the only team to start Ligue 1 with two wins.
Fiery Flanders derby in Belgium
Gent handed Belgian Pro League champions Club Brugge their first defeat of the season, winning 2-1 thanks to a late goal from Ibrahima Cissé.
Cissé was sent off in stoppage time for striking an opponent with his elbow.
Brugge's Portuguese winger Carlos Forbs was sent off earlier, before Cissé's 85th-minute headed winner. Both Flanders rivals finished with 10 men.
Sporting Charleroi lead the table with four wins from four games.