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A second consecutive victory took Barca up to fifth on 20 points after 12 games and knocked Real Sociedad off the top and into second.
Arsenal lost 1-0 at home to Burnley -- a fourth successive home league defeat for the first time since 1959 leaving the Gunners languishing down in 15th spot.
Harry Kane scored his 250th career goal for club and country after laying on Son Heung-min's 10th league goal of the season as Tottenham beat Arsenal 2-0 to reach 24 points from 11 games.
Edinson Cavani came off the bench to score twice for Manchester United who overturned a 2-0 half-time deficit at Southampton to win 3-2 -- a club-record eighth successive away league win moving them into the top half.
Liverpool are now unbeaten in 64 league games at Anfield setting a new club record and they were full value for the win.
Germany were powerless to stop Luis Enrique's relentless side as the visitors suffered their worst defeat in a competitive game and the most humiliating since losing by the same scoreline against Austria in a friendly in 1931.
A late equaliser from Jannik Vestergaard earned Southampton a 3-3 draw away to Chelsea.
Germany scored once in either half to beat hosts Ukraine 2-1.
Jerry Quy, who had a role as an away supporters' liason as well as entertaining home fans at the Emirates Stadium as the green dinosaur, was recently let go by the club due to the impact of the COVID-19 pandemic, according to British media reports.
Champions Liverpool were ripped apart 7-2 at Aston Villa and Manchester United were routed 6-1 at home by Tottenham Hotspur.