Arnaut Danjuma gave the visitors a third-minute lead in a match postponed on Wednesday by heavy snow.
Etienne Capoue added a second before half-time and Danjuma made it 3-0 six minutes after the restart.
Ruslan Malinovskyi and Duvan Zapata responded for Atalanta, who were unable to earn the victory they required.
As runners-up Villarreal will be one of the eight unseeded sides in Monday’s draw, while Atalanta will enter the Europa League knockout round play-off draw.
Already in second place, Unai Emery’s Villarreal needed a point to join group winners Manchester United – whose 1-1 draw with Young Boys eliminated the Swiss club – in the knockout stage.
They made the perfect start when Danjuma raced on to Dani Parejo’s pass and slotted through the legs of Juan Musso with the first chance of the match.
With only three points enough for Atalanta, things got even worse for the Serie A side as Capoue beat Musso at his near post and Danjuma scored again with a smart turn and finish to leave the Italians requiring four goals in 39 minutes.
They managed to get two against an increasingly shaky looking Villarreal, Malinovskyi drilling in from the edge of the box and Zapata lifting the ball over the onrushing Geronimo Rulli with 10 minutes remaining.
But, with Luis Muriel rattling the post in the closing stages, Gian Piero Gasperini’s side ultimately fell short of producing a remarkable comeback.