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Sadio Mane scored twice while Mo Salah and Xherdan Shaqiri got the other goals to lift Juergen Klopp's side three points ahead of Manchester City, who play at Tottenham on Monday.
The victory took Liverpool to 26 points from 10 games, equalling their tally from 2008-09.
Bournemouth moved within a point of fifth-placed Tottenham with a 3-0 win at Fulham while Watford are one point further back in seventh after a 3-0 win over Huddersfield, who fell to bottom spot.
Salah opened the scoring on 10 minutes at Anfield with his seventh goal of the season and Mane doubled their lead midway through the second half.
Calumn Paterson gave Cardiff hope 13 minutes from time but substitute Shaqiri and Mane, with his second, completed an eventually comfortable victory.
"We had very good moments, a lot of them, and periods where we could have done better," Klopp said.
"We scored the second one and we conceded a goal which is never something you want.
"It possibly helped actually as Cardiff believed they could do more and we finished the game. Now we can recover and prepare for the next game."
Callum Wilson scored twice, the first from the penalty spot, and David Brooks got the other as Bournemouth poured more pressure on Fulham manager Slavisa Jokanovic.
Bournemouth climbed to within a point of the top five but Fulham have now lost four straight Premier League games.
"We have enough quality to score but we can't find a way to find a clean sheet," Jokanovic said.
"The Premier League is tough not just for us but for many clubs. We are making expensive mistakes.
"I am not thinking about my future. I will be ready for the next challenge. I am living my present and that is today a very hard defeat. I must be brave and keep going and encourage my team."
Huddersfield dropped to the bottom of the table after a 3-0 defeat at Watford.
Roberto Pereyra dribbled through half of the Huddersfield defence to score the opener, Gerard Deulofeu got the second and Isaac Success finished it off with the third late on.
"I am disappointed because in recent weeks we had defended better, but it was our worst performance defensively for a while," Huddersfield manager David Wagner said.
"We created chances, but didn’t have the luck when we hit the bar (early on). If we want to collect points we have to do well offensively and defensively.
"Next week against Fulham is a belter and an opportunity that we have to use."
Brighton manager Chris Hughton was indebted to a goal from Glenn Murray for their 1-0 win over Wolves, even if they didn't play as well as they have in recent weeks.
"I am delighted, we had to really earn it against a very good side," Hughton said.
"We are not playing at our best, nowhere near. We have players who are not at their level, we are not good on the ball but we are defending really well."
Newcastle picked up a vital point with a 0-0 draw at Southampton, enough to lift them off the bottom of the table.
It is only the second time in Newcastle's history that they have not won any of their 10 league matches, 120 years after the first.
"In the circumstances it is a positive result, a clean sheet and one point away," Newcastle manager Rafael Benitez said.
"We are in a difficult position but it is a small stop forward in terms of confidence and showing team we can compete and do what expecting to do.
"The team is working hard so I can not complain."
The victory took Liverpool to 26 points from 10 games, equalling their tally from 2008-09.
Bournemouth moved within a point of fifth-placed Tottenham with a 3-0 win at Fulham while Watford are one point further back in seventh after a 3-0 win over Huddersfield, who fell to bottom spot.
Salah opened the scoring on 10 minutes at Anfield with his seventh goal of the season and Mane doubled their lead midway through the second half.
Calumn Paterson gave Cardiff hope 13 minutes from time but substitute Shaqiri and Mane, with his second, completed an eventually comfortable victory.
"We had very good moments, a lot of them, and periods where we could have done better," Klopp said.
"We scored the second one and we conceded a goal which is never something you want.
"It possibly helped actually as Cardiff believed they could do more and we finished the game. Now we can recover and prepare for the next game."
Callum Wilson scored twice, the first from the penalty spot, and David Brooks got the other as Bournemouth poured more pressure on Fulham manager Slavisa Jokanovic.
Bournemouth climbed to within a point of the top five but Fulham have now lost four straight Premier League games.
"We have enough quality to score but we can't find a way to find a clean sheet," Jokanovic said.
"The Premier League is tough not just for us but for many clubs. We are making expensive mistakes.
"I am not thinking about my future. I will be ready for the next challenge. I am living my present and that is today a very hard defeat. I must be brave and keep going and encourage my team."
Huddersfield dropped to the bottom of the table after a 3-0 defeat at Watford.
Roberto Pereyra dribbled through half of the Huddersfield defence to score the opener, Gerard Deulofeu got the second and Isaac Success finished it off with the third late on.
"I am disappointed because in recent weeks we had defended better, but it was our worst performance defensively for a while," Huddersfield manager David Wagner said.
"We created chances, but didn’t have the luck when we hit the bar (early on). If we want to collect points we have to do well offensively and defensively.
"Next week against Fulham is a belter and an opportunity that we have to use."
Brighton manager Chris Hughton was indebted to a goal from Glenn Murray for their 1-0 win over Wolves, even if they didn't play as well as they have in recent weeks.
"I am delighted, we had to really earn it against a very good side," Hughton said.
"We are not playing at our best, nowhere near. We have players who are not at their level, we are not good on the ball but we are defending really well."
Newcastle picked up a vital point with a 0-0 draw at Southampton, enough to lift them off the bottom of the table.
It is only the second time in Newcastle's history that they have not won any of their 10 league matches, 120 years after the first.
"In the circumstances it is a positive result, a clean sheet and one point away," Newcastle manager Rafael Benitez said.
"We are in a difficult position but it is a small stop forward in terms of confidence and showing team we can compete and do what expecting to do.
"The team is working hard so I can not complain."
