That result meant they have won 13 out of 14 matches so far this season, the best ever start by anyone to a league game.
Barcelona are now six points clear of Atletico Madrid and 11 from champions Real Madrid.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.