Chelsea were three goals ahead inside 17 minutes against the disappointing Magpies, before Pedro added his second just before the hour. Bertrand Traore also got in on the action late on to net his first Premier League goal, but there was a late consolation for Newcastle through Andros Townsend.
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Chelsea boss Guus Hiddink recalled Eden Hazard and Pedro to his starting XI, while there was a spot for Gary Cahill at centre-back due to Kurt Zouma's absence with a serious knee problem. As for Newcastle, head coach Steve McClaren kept faith with the same XI that beat West Bromwich Albion last weekend.
The home side had a half-chance inside the first two minutes when Townsend could only clear to Nemanja Matic outside the Newcastle box, but the midfielder's effort was always wide of the post.
Just four minutes later, it was 2-0 Chelsea when a short Rolando Aarons pass was gobbled up by Pedro, who carried the ball towards the Newcastle box before finding the back of the net with a smart finish.
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It got worse for the visitors in the 17th minute when Costa drove away from Fabricio Coloccini before picking out a clever pass in to Willian, who was never going to miss from close range.
Branislav Ivanovic had the chance to make it four for Chelsea in the 25th minute after meeting a low cross from Pedro, but Aarons was on hand to make the block as the Magpies continued to struggle at both ends. John Terry was next to come close for the dominant hosts, but his goal-bound header was blocked by Taylor.
Newcastle's best chance of the first period fell to Georginio Wijnaldum in the 35th minute, but the Dutchman's effort from a Daryl Janmaat cross was straight at Thibaut Courtois, before Pedro fired straight at Elliot down the other end.
Willian also came close with a free kick late in the half, but it was not all good news for Chelsea in the first period, however, with skipper Terry forced off with a muscular problem, which will be a concern ahead of the Champions League last-16 first leg against Paris Saint-Germain on Tuesday.
Jonjo Shelvey had the first opportunity of the second period, but the Newcastle midfielder's goal-bound strike from inside the Chelsea box was blocked by Cahill, before Mitrovic fired just wide just before the 60-minute mark.
It was Chelsea that added a fourth in the 59th minute, however, when Pedro collected a long pass from Cesc Fabregas before placing his effort into the bottom corner.
Chances were few and far between as the match headed for its final 15 minutes, but the damage had already been done in the first half and Newcastle were wary of conceding a fifth having seen their goal difference take a hit.
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The home side were not finished, however, and had their fifth seven minutes before full time when Traore converted a Cesar Azpilicueta cross to score his first Premier League goal for the club.
It should have been 6-0 in the latter stages when Fabregas set up Hazard with another sweeping pass, but the Belgian could only poke wide of the post from close range.
Newcastle did manage to net a consolation in the final minute, however, when Townsend beat Courtois after a mazy run.
Chelsea, who are unbeaten in their 10 league games since Hiddink took charge, now have three days to prepare for their Champions League clash with PSG, but Newcastle will not return to action until travelling to Stoke City on March 2.