England thumped by Hungary as relegation looms
First-half goals from Cody Gakpo and Noa Lang put the hosts two up, but a Brennan Johnson goal and a stoppage-time Bale spot-kick looked to have earned Wales a draw.
However, Oranje talisman Depay subsequently grabbed a winner to spark wild celebrations in the home ranks.
A third victory in four matches at the end of a long season continued a strong Nations League campaign for the Netherlands, who remain top of the group while Wales are bottom and winless.