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Marten de Roon, Cody Gakpo and Wout Weghorst scored before the break as the Dutch won a second match in Group B, showing much improvement after crashing out of the Nations League finals they hosted in June.
They now have six points, ahead of Greece on goal difference, behind leaders France who have won five out of five.
The Dutch victory came after coach Ronald Koeman had challenged his team to show more of a steely edge after losing three of four games since he took charge at the start of the year.
De Roon scored the first goal after 17 minutes as he thumped home a ball headed down by Denzel Dumfries from a corner to register his first international goal.
Gakpo was unmarked at the back post as the Greek defence was badly exposed and finished off a clever cross from Dumfries, who completed a hat-trick of assists as he provided Weghorst with a chipped cross to head home with a diving effort in the 39th minute.
Dumfries could have had a goal of his own but was denied by the post in the 36th minute while Xavi Simons’ swerving shot in the 28th minute produced a miraculous one-handed stop from Greek goalkeeper Odysseas Vlachodimos.
The second half was light on chances but the damage was done as the Greeks suffered their heaviest defeat since Gustavo Poyet took over as coach some 18 months ago.
The Dutch face a key qualifier in Dublin on Sunday against Ireland, who lost 2-0 to France on Thursday. Greece host Gibraltar in Athens on Sunday.