That win takes them top of the final six team qualifying section, ahead of Costa Rica.
Costa Rica were held 0-0 by Mexico, who remain third but have played a game more than the teams above them.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.