Goals from Gary Cahill and Diego Costa helped the west London side seal the three points on Merseyside after Emre Can had given the hosts an early lead.
Liverpool had shouts for a second-half penalty waved away by referee Anthony Taylor after Cahill appeared to handle Steven Gerrard’s shot in the box.
Saturday’s big game inevitably prompted plenty of activity on Twitter – and here are some of our favourite post-match updates.
Celebrity Arsenal fan Piers Morgan (@piersmorgan) is not a happy man: “Switching to the rugby. Hate watching Chelsea win.”
Ex-Liverpool defender Jamie Carragher (@Carra23) wasn’t impressed by the Reds’ tactics: “Chelsea defend for their lives brilliantly. Hazard is a star. Lfc caused themselves problems all day playing from the back (except for goal)”
England legend Gary Lineker (@GaryLineker) is looking forward to seeing Daniel Sturridge back for Liverpool: “Another win for relentless Chelsea. Brendan’s plans haven’t worked, but doesn’t take someone who’s managed to see LFC need @D_Sturridge”
Former Arsenal man Lee Dixon (@LeeDixon2) is impressed by what he’s seen of Chelsea this season: “Yes Chelsea had some luck with the penalty but they are head and shoulders the best TEAM by far in League”
Ex-England cricketer Alec Stewart (@StewieCricket) is pleased with the win: “Another great win for Chelsea. Liverpool should have had a penalty but it can’t disguise how much they’re struggling. Can’t live off history.”
Former Liverpool midfielder Dietmar Hamann (@DietmarHamann) says the result is a fair one: “Liverpool beaten fair and square, no complaints. Chelsea by far the better side. Long way to go but Sturridge needs to come back soon.”
And finally, Phil Neville (@fizzer18) asks a good question: “Is this the best chelsea team Mourinho as built??”
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