The hard-fought win took Zinedine Zidane's side on to 77 points after 34 games, seven clear of second-placed Barca who visit in-form Villarreal later on Sunday.
Here is a summary of stories from the English Premier League
A summary of Saturday's action in Serie A and La Liga.
A makeshift England side beat Romania 1-0 in their final Euro 2020 warm-up game, while Belgium's Romelu Lukaku underlined his status as one of the world's top strikers with his 60th international goal to secure a 1-0 win over Croatia.
Czech Republic goalkeeper Petr Cech ended a highly successful 11-year spell at English champions Chelsea when he moved to Premier League rivals Arsenal on Monday.
Lionel Messi scored his maiden goal for Paris St Germain in Tuesday's 2-0 Champions League victory against Manchester City.
Chelsea's Spanish striker Diego Costa was named along with usual suspects Lionel Messi and Cristiano Ronaldo in the 23- man FIFA Ballon D'Or short-list released on Tuesday.
Images from Saturday's action in La Liga.
IMAGES from the FIFA World Cup first semi-final played between France and Belgium on Tuesday
Real Madrid showed their character by beating Barcelona 2-0 in Sunday's top-of-the-table 'Clasico', leapfrogging their rivals at the La Liga summit after a week in which their pride had taken a beating at home and in Europe. Brazilian teenager Vinicius Jr scored the opener in the 71st minute with a strike that deflected off Gerard Pique, flummoxing goalkeeper Marc-Andre ter Stegen who had made some jaw-dropping saves, and substitute Mariano added the second in added time.
Real have three days to recover from the humbling defeat before Saturday's crunch local derby against Atletico Madrid
Images from the World Cup qualifying matches played on Wednesday night.
Arsenal cruised to a 3-0 win over Chelsea on Saturday, scoring all three goals in the first half to claim their first Premier League victory over their London rivals in 10 attempts. Arsenal gave their manager Arsene Wenger something to celebrate as he marked 20 years in charge of the club, punishing Chelsea for poor defending to race into a 2-0 lead within 15 minutes.
There was eye-catching sports action the world over and we summarise it all in this breathtaking photo feature...
Chelsea's Jose Mourinho, who hoped to celebrate his new contract with victory at an expectant Stamford Bridge, ended up grateful his team did not become the first Premier League champions to start their title defence with a defeat.
The win took second-placed Real to 62 points after 29 games, two behind champions Barca who beat Leganes 2-0 on Tuesday.
Barca feel familiar February blues as tiredness sets in
Images from Wednesday's action in the UEFA Champions League.
Tottenham Hotspur denied Chelsea a record 14th consecutive Premier League win and loosened their grip on the title race as two Dele Alli headers secured a 2-0 victory.
Images from football matches played across Europe on Sunday.
Hazard collected 53 percent of the vote making him a comfortable winner, while he and Terry's Chelsea team mates Cesc Fabregas, Branislav Ivanovic and goalkeeper Thibaut Courtois also featured in the top 10.
A fortunate 85th-minute goal from Brazilian Willian earned Premier League champions Chelsea a 1-1 draw at Liverpool on Saturday after Mohamed Salah's 15th goal of the season looked to have given the hosts the three points.
Real Madrid clinched a record-extending 34th La Liga title with one game to spare by beating Villarreal 2-1 at home on Thursday thanks to two goals from their leading scorer Karim Benzema. Real have 86 points after 37 games, seven more than deposed champions Barcelona who were beaten 2-1 at home to Osasuna.
Brazil's Willian told reporters he will be doing everything he can to send his team mate Eden Hazard home early from Russia.
Venkatesan has decided to pursue opportunities outside Microsoft, Microsoft said in a statement.
Late goals from Eden Hazard and Nemanja Matric sealed a 4-2 victory for Chelsea over London rivals Tottenham Hotspur in a rip-roaring FA Cup semi-final at Wembley on Saturday.
A stunning strike from Jordan Henderson helped Liverpool secure a comfortable 2-1 win at Chelsea on Friday that ended the London club's unbeaten start to the season and underlined the growing potential of Juergen Klopp's side.
Chelsea wrapped up their pre-season tour of the United States on a high note by beating Barcelona in a shootout after their International Champions Cup match ended 2-2 on Tuesday.
Cristiano Ronaldo, Luka Modric and Mohamed Salah were named as the three finalists.
Chelsea manager Jose Mourinho has been a named a respondent in the legal action being brought against the club by their former team doctor Eva Carneiro for constructive dismissal, sources close to the case said on Monday.
Images from the FIFA World Cup qualifying matches on Sunday night.
Luka Modric pulled one back for Zinedine Zidane's shellshocked side with a brilliant strike from distance early in the second half before substitute Vinicius Jr reduced the deficit to one goal.
Real Madrid overcame an early howler from Sergio Ramos to beat Real Sociedad 3-1 at home on an eventful Saturday at the Santiago Bernabeu, where Gareth Bale was loudly booed by his own supporters and Luka Modric returned to his very best form.
IMAGES from the Champions League matches played on Wednesday.
Second-half headers from Diego Godin and Raul Garcia gave holders Atletico Madrid a 2-0 win over Valencia and a place in the King's Cup quarter-finals by 3-1 on aggregate.
The European champions, who were humbled 3-0 by tiny Eibar last week, took a fortuitous lead when Valencia midfielder Daniel Wass nodded a Dani Carvajal cross into his own net in the eighth minute after former Arsenal defender Gabriel Paulista had failed to clear the danger.
Arsenal denied Chelsea the double with a 2-1 victory in an enthralling FA Cup final.
Chelsea have enough experience to keep their composure in the title race after Sunday's 2-0 defeat at Manchester United cut their lead at the top of the Premier League table to four points with six games left, goalkeeper Asmir Begovic has said.
Images from the Champions League matches played on Wednesday
Former Arsenal striker Ian Wright has launched a scathing attack on the club's manager Arsene Wenger, saying he could not make a case for the Frenchman to extend his reign beyond this season.
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