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. "It makes it even more intense, good for the people."
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.
MANE DOUBLE
Salah, who scored his 50th Liverpool goal midweek, gave his team a 10th-minute lead against Cardiff. They didn't score again for nearly an hour, when Mane raced on to a pass from Alberto Moreno to smash the ball into the top corner.
Callum Paterson pulled one back for the visitors, preventing Liverpool from a 10th successive league cleansheet at Anfield. But substitute Shaqiri made it 3-1 after more good work from Salah, who was also involved in the fourth, setting up Mane.
Manager Juergen Klopp praised Mane, who has featured in the last two games despite a broken left thumb.
"He plays with a brace," Klopp said. "I wouldn't feel comfortable with it, but he ignores it pretty well."
SOLO GOAL
Watford, with 19 points from 10 games, eclipsed its previous best start in the top-flight in 1982, the season it finished second.
Roberto Pereyra produced a brilliant solo goal to kick start a dominant display against winless Huddersfield. The former Juventus winger dribbled past several defenders to open the scoring after 10 minutes.
Gerard Deulofeu added the second, and Isaac Success used a clever free kick routine.
VARDY OMISSION
Fabian Balbuena gave West Ham a 30th-minute lead at Leicester, but the visitors were reduced to 10 men eight minutes later when Mark Noble was sent off for a bad challenge on Wilfred Ndidi.
Puel sent on Vardy at halftime and the former England forward spurned two scoring chances before Ndidi equalized with two minutes to go.
Leicester's Daniel Amartey was carried off on a stretcher late on after he appeared to get his studs caught in the turf.
WILSON DOUBLE
Bournemouth striker Callum Wilson converted an early penalty at Fulham after being brought down by Timothy Fosu-Mensah. David Brooks made it 2-0.
Fulham midfielder Kevin McDonald was sent off in the 73rd, and Bournemouth took advantage with a second goal for Wilson, set up by Ryan Fraser.
OTHER MATCHES
Brighton secured a third straight league win, at Wolverhampton's expense, while Southampton and Newcastle, who have only one win between them in 20 games, showed why in a dire match.
The good news for Newcastle was the point lifted it off the bottom of the table, above Huddersfield.