The Dutch international put Atalanta ahead inside three minutes and Etienne Capoue doubled the lead shortly before half-time on another chilly evening in Bergamo.
Danjuma scored again early in the second half but Villarreal were forced to hold on as Atalanta responded with goals from Ruslan Malinovskyi and Duvan Zapata while hitting the woodwork three times.
Spanish club Villarreal finished as runners-up to Group F winners Manchester United, with Atalanta going into the Europa League knockout-round play-offs in February.
Quarter-finalists two seasons ago, Atalanta needed a victory to climb above Villarreal into second place in the group but made a disastrous start to a game pushed back from Wednesday after a cold snap swept across regions of northern Italy.
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