Chelsea had served notice of their title credentials with an impressive 1-0 win at City on Monday and they were quick to take control against Newcastle despite captain John Terry missing out with a muscular strain.
Hazard broke the deadlock in the 27th minute with a first-time finish from a Branislav Ivanovic pass and the Belgian added a second seven minutes later following a neat back-heel by Samuel Eto'o.
A foul on Eto'o by Mapou Yanga-Mbiwa presented Hazard with an opportunity to complete his first Chelsea hat-trick from the penalty spot in the 63rd minute and he duly obliged by sending Tim Krul the wrong way.
"I know today we are top of the league, but I look to fifth place," Chelsea manager Jose Mourinho said.
"I look to Tottenham v Everton and Manchester United v Fulham tomorrow (Sunday) and I want to be far from fifth.
Man City held at Norwich, Swansea win South Wales derby
Victory took Chelsea a point above Arsenal and two points clear of City, who were unable to repeat their 7-0 annihilation of Norwich from earlier in the season.
Manuel Pellegrini's side dominated proceedings at Carrow Road, but in the continued absence of top scorer Sergio Aguero they came no closer to scoring than a first-half Alvaro Negredo header that hit the crossbar.
"We are frustrated because we could not win, but we did all we could and in front of us there was a team who defended very well," City manager Pellegrini said.
"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."
Laudrup was sacked as manager on Tuesday and replaced by former captain Garry Monk, who saw Wayne Routledge, Nathan Dyer and Wilfried Bony plunder second-half goals that left Cardiff rooted in the bottom three.
January signings Tom Ince and Joe Ledley marked their Palace debuts with goals, only for West Brom debutant Thievy Bifouma to hit back, but Marouane Chamakh sealed victory with a penalty mid-way through the second half.
Sunderland had Wes Brown sent off after three minutes in a 2-0 loss at home to Hull City that saw them fall to within one place of the drop zone, while Stoke City twice came from behind to force a 2-2 draw at Southampton.