Manchester City moved up to second despite a bizarre Vincent Kompany own goal in a 4-2 victory at lowly Fulham while champions Manchester United, in seventh, overcame West Ham United 3-1 through Danny Welbeck, Adnan Januzaj and Ashley Young.
The irrepressible Suarez, who looked to be heading out of Anfield in the close season following a ban for biting an opponent, expertly volleyed in the opener before setting up Raheem Sterling for the second after a superb ball from the resurgent Jordan Henderson.
It was soon 3-0 as the 26-year-old Suarez netted his 19th league goal of the season on the stroke of halftime with a superb curling shot from the edge of the box following more Henderson magic with a back-heel.
Liverpool hammered Tottenham Hotspur 5-0 away last weekend and could have had more against Cardiff with Suarez almost completing a hat-trick when he clipped the post.
"I am happy with the new contract but I was focused on the game. We played very well in the first half," the Uruguay striker told BT Sport television.
"It's too early to say (we can win the title). It is important we work for the next game. When we play at home we are strong."
The easy win over sixth from bottom Cardiff, and their beleaguered manager Malky Mackay, sent Liverpool a point clear at the top with 36 from 17 games.
Arsenal (35 points), who are third, can take back first position by winning at home to fourth-placed Chelsea (33) on Monday (2000 GMT).
Suarez, again captain in the continued absence of the injured Steven Gerrard, penned a long-term deal on Friday as Liverpool try to build on a strong start and finally challenge for the title again after years of woe.
Facing one of the in-form players in world football was not what Mackay wanted at the end of a week when media reports said he had been asked to resign or be sacked by Malaysian owner Vincent Tan despite gaining promotion last season.
Cardiff fans should have been enjoying the trip to famous Anfield in their debut Premier League season but instead held up 'Tan Out' banners and booed the controversial sunglasses-wearing tycoon who has also recently switched the club kit from the traditional blue to red.
The clubs had only previously met in the league in 1959, when Liverpool great Bill Shankly took charge for the first time as Cardiff won 4-0 away.
That was never going to happen on Saturday but Jordan Mutch did pull a goal back for the visitors in an improved second- half show.
Manchester City (35 points) moved above Arsenal on goal difference after a patchy performance that underlined their problems away from home this season.
Another Yaya Toure free kick on 23 minutes and Kompany's goal at the right end of the field put City 2-0 up at second from bottom Fulham.
The home team equalised after the interval with a goal from Kieran Richardson and when Kompany sent an attempted clearance spiralling into his own net.
Jesus Navas restored City's lead in the 78th minute and poor defending allowed James Milner to make it 4-2.
City and England goalkeeper Joe Hart made his first league start since Oct. 27 having been dropped in favour of Romania's Costel Pantilimon who was on the bench this time following last weekend's 6-3 win over Arsenal.
Manchester United were never in any danger against fast-dropping West Ham, Welbeck adding to his two goals from last weekend's 3-0 victory at Aston Villa with a neat finish although debut Spanish keeper Adrian could have done better.
Young winger Januzaj, a rare bright spot in a difficult season for United after David Moyes took over as manager from Alex Ferguson, then grabbed his first Old Trafford goal.
After the break Young defied his critics by blasting home another cracker and Carlton Cole netted for West Ham.
Sixth-placed Newcastle United sealed a sixth victory in eight games with a 3-0 win at third from bottom Crystal Palace.
Stoke City rose to 10th after a 2-1 triumph at home to Aston Villa, Peter Crouch hitting the winner against his former club.
Managerless West Bromwich Albion began life without Steve Clarke, after his surprise sacking last weekend, with a 1-1 draw at home to Hull City thanks to Matej Vydra's late equaliser.
Wes Brown hit the post and was also sent off for a rash challenge late on as Sunderland drew 0-0 at home to Norwich City to leave Gus Poyet's side bottom at Christmas - something that normally implies doom come the end of the season.
