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Cardiff manager Neil Warnock said before his team's visit to Anfield it was "virtually impossible" for any side to win there this season.
Sadio Mane led with two goals, and Mohamed Salah and Xherdan Shaqiri also struck as unbeaten Liverpool went three points clear of second-place Manchester City, which plays Tottenham on Monday at Wembley Stadium.
Liverpool is also five ahead of Tottenham, Chelsea, and Arsenal. Chelsea visits Burnley on Sunday, when Arsenal travels to London rival Crystal Palace.
"It is unbelievable five or six clubs have such a big number of points," Liverpool manager Juergen Klopp said.
Watford achieved its best start in a top-flight campaign after beating Huddersfield 3-0, while Leicester manager Claude Puel caused a surprise by dropping talismanic striker Jamie Vardy to the bench while the rest drew with West Ham 1-1 at home.
Bournemouth cruised past Fulham 3-0, and Glenn Murray's 100th goal for Brighton beat Wolverhampton 1-0. Southampton's game with Newcastle ended in a goalless draw at St. Mary's.
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