The hosts went ahead early on through a Neymar volley, who then set up Jo in injury time for the second.
But in between it was Mexico who played the better football, and who were unlucky to lose.
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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.