Kolbeinn Sigthorsson opened the scoring for Ajax before Tim Gilissen netted an own goal.
Ajax can win the title next week if they beat Willem II at home in their penultimate game.
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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.