High-scoring Manchester City, who started the day in second place and could have gone top, slipped to third after failing to find the net for the second successive game in a 0-0 draw at Norwich City who defended heroically for most of the match.
With 13 games remaining, Chelsea are top with 56 points, followed by Arsenal on 55, City with 54 and Liverpool on 50.
Everton (45) and Tottenham Hotspur (44), who are fifth and sixth respectively, meet at White Hart Lane on Sunday.
Chelsea, described by manager Jose Mourinho this week as "the little horse" competing against the "big horses" of Arsenal and City, got their noses in front in the most open title race for years with a comprehensive win over Newcastle.
The visitors had no answer to Hazard's artistry with the Belgian playmaker scoring in the 27th and 34th minutes with his third goal coming from the penalty spot after striker Samuel Eto'o was fouled by Mapou Yanga-Mbiwa.
Mourinho though was unhappy with Chelsea's first half performance despite them leading 2-0 at the break although he praised Hazard and said he could not understand why he had not won a Player of the Month Award yet this season.
"We gave them too much freedom to play," he told Sky Sports, "but after that we completely controlled the game."
Asked what he thought of Hazard's fine individual display Mourinho said: "He is a player that for some reason has not had one single Player of the Month in this Premier League.
"That is quite surprising for me. Perhaps this country is so full of tremendous players that he hasn't had an award."
ARSENAL CRUSHED
In the early game, Liverpool made a mockery of Arsenal being top, crushing them with a stunning display of attacking football that produced four goals in an astonishing first 20 minutes from Martin Skrtel (2), Raheem Sterling (2) and Daniel Sturridge.
Mikel Arteta scored a second half consolation for the Gunners from the penalty spot.
The victory put Liverpool back in the title race and as Arsenal manager Arsene Wenger conceded afterwards, raised questions about his side's title ambitions.
Arsenal had only conceded four goals in their last eight unbeaten league matches, before Liverpool went on the rampage.
Despite the emphatic win and Liverpool's total dominance, which led bookmakers to cut the Merseyside club's title odds from 25-1 to 12-1, coach Brendan Rodgers played down any talk of winning the league.
"Everything about our game was incredible today, it was an amazing performance against an outstanding team. To be fair, the title has not been a target, but we are improving and everything we did today was outstanding," he told BT Sport.
Wenger said: "It was a very poor day. Of course, it raises some questions today because we were caught many times and were naive."
Arsenal will have a quick chance of avenging their first league defeat at Anfield since 2007 when the two sides meet in an FA Cup fifth round tie at the Emirates next weekend.
MORAL VICTORY
Although Norwich and Manchester City failed to produce a goal at Carrow Road, the result was something of a moral victory for the home side who had lost 7-0 at The Etihad in November.
The visitors, who have 68 league goals this season and 115 in all matches, also failed to score in a 1-0 home defeat by Chelsea on Monday and only had two shots on target on Saturday.
Coach Manuel Pellegrini told the BBC: "We are frustrated because we could not win, but we did all we could do but in front of us there was a team who defended very well.
"Every team will drop points, but we are still two points behind the leaders and we have 39 points to play for so we will continue exactly the same.
Although there were no goals at Norwich there were plenty everywhere else which had a big impact on the bottom half of the table where eight of the 11 sides played each other.
There were wins for Crystal Palace, who beat visiting West Bromwich Albion 3-1 with debutants Thomas Ince and Joe Ledley among the scorers, while West Ham United improved their chances of staying up with a Kevin Nolan double securing a 2-0 victory at Aston Villa.
Palace climbed to 13th and West Ham to 14th but Sunderland's relegation fears increased with a 2-0 home defeat by Hull City, after defender Wes Brown was sent off in the third minute for his third dismissal of the season, and they stand only a point above West Brom who slipped into the bottom three.
