Newcastle’s 12th defeat of the season leaves the Magpies just one point better off than Chelsea in 10th.
The pressure is also rising on Eddie Howe as Saudi-backed Newcastle have failed to build on finishing fourth last season to qualify for the Champions League for the first time in 20 years.
Pochettino, though, was facing more open revolt from among his own support.
Chelsea fans called for the Argentine’s dismissal during a 2-2 draw at Brentford last weekend.
The former Tottenham boss has suffered a difficult first season in charge, which included losing the League Cup final to a severely depleted Liverpool last month.
But there were promising signs for Pochettino as some of his much-criticised expensive young recruits showed glimpses of their potential.
Jackson is now up to 12 goals in his debut season as he cleverly flicked in Palmer’s shot after less than six minutes.
However, it was the story of Chelsea’s season that they failed to build on that flying start and allowed Newcastle to go onto control the rest of the first half.
The visitors were dealt an injury blow midway through the first period when Anthony Gordon was forced off.
But Alexander Isak produced a quality finish, fired low into the far corner, to bring Newcastle level two minutes before half-time.
The one new signing Chelsea have been able to rely on all season is Palmer and the England international restored his side’s lead in emphatic fashion just before the hour mark.
Palmer collected Enzo Fernandez’s pass, cut inside and unleashed a powerful effort for his 11th Premier League goal of the season.
Mudryk, by contrast, has been a constant frustration for a number of Chelsea managers since joining for £88 million ($113 million) just over a year ago.
The Ukrainian had been on the pitch only five minutes when showed his blistering pace to burst through the heart of the Newcastle defence and turn in just his sixth goal in 46 Chelsea appearances.
Jacob Murphy’s rocket of a shot into the top corner set up a nervy finish for the hosts.
But it was too little, too late for the visitors in the latest disappointment of an underwhelming campaign.
© Agence France-Presse
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