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The visitors controlled possession early on, coming close to an opener on 17 minutes when Bas Dost tested Wales keeper Wayne Hennessey with a header, before Wales forward Tom Lawrence forced a save from Jasper Cillessen at the other end of the pitch.
The Netherlands took the lead on 32 minutes through Dost, as the Wolfsburg striker connected with an inviting Daryl Janmaat cross to head past Hennessey for his first international goal.
Danny Blind's side controlled the remainder of the first half, but conceded an equaliser against the run of play when Terence Kongolo handled the ball inside his own penalty area. Cillessen denied Joe Allen from the resulting penalty, only for Joe Ledley to pounce on the rebound and fire past the Ajax man.
After the break the Netherlands regained control of the match, and almost restored their lead on 48 minutes when Wesley Sneijder played in Robben, who forced a good save from Hennessey.
Six minutes later the Bayern Munich man managed to find the back of the net, beating a number of Wales defenders before cutting inside from the right to place an effort in the bottom corner of the goal.
The hosts responded well to going behind, coming close to an equaliser moments later when George Williams dragged an effort wide following some good work from Lawrence.
Wales scored their second of the evening on 70 minutes through Huddersfield Town midfielder Emyr Huws, who connected with a Joe Allen cross to head past Cillessen.
Arjen Robben missed a good opportunity to net a second goal moments later, missing the target from inside the penalty area after a Welsh defensive mix-up.
The winger wrapped up the victory for his side on 81 minutes, meeting Dost's through-ball before firing past substitute goalkeeper Owain Fon Williams.