The Dutch international put Atalanta ahead inside three minutes and Etienne Capoue doubled the lead shortly before halftime 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.
Villarreal finished as runners-up to Group F winners Manchester United, with Atalanta going into the Europa League knockout-round play-offs in February.
Quarterfinalists two seasons ago, Atalanta needed a win 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 northern Italy.
Merih Demiral lost possession and Dani Parejo sent Danjuma clear of the Atalanta defence to slot between the legs of goalkeeper Juan Musso.
Atalanta captain Rafael Toloi headed over from a free-kick and Remo Freuler drew a flying save from Geronimo Rulli, but Villarreal made it 2-0 as Capoue controlled inside the area and drilled home.
Gerard Moreno set up Danjuma to grab Villarreal's third on 51 minutes, seemingly ending any hopes for Atalanta.
Malinovskyi clipped the bar just before the hour with a free-kick and Zapata shaved the outside of the post.
The hosts eventually pulled one back via Malinovskyi's deflected drive with 20 minutes to play and Zapata dinked over the advancing Rulli to give Atalanta hope.
Zapata headed straight at Rulli before Luis Muriel rattled the post as Atalanta laid siege to the Villarreal goal but the comeback ultimately fell short.
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