The Toffees themselves were ending a spell out of continental competition and made six changes against a La Dea team who were playing in the unfamiliar surroundings of Reggio Emilia's Mapei Stadium.
Gian Piero Gasperini's men finished fourth in Serie A last term and despite losing a number of their stars, have rebuilt nicely and their fans who made the 120 mile trip from Bergamo, where the club's ground has been deemed unsuitable by UEFA, certainly made themselves heard.
The home side started well but it was Everton with the first effort, Gylfi Sigurdsson stinging the palms of Etrit Berisha from the edge of the area, while Wayne Rooney also went close.
Andrea Massiello then should have opened the scoring when he saw his close range effort well saved by Maarten Stekelenburg but the defender made amends seconds later when he stabbed home at the back post from the resulting corner after 27 minutes.
It was all Atalanta after that and Alejandro Gomez curled in a brilliant second with four minutes of the half left and then Bryan Cristante made it three just before the break.
A 3-0 lead was everything La Dea deserved and despite the Toffees doing their best to raise their game, Atalanta remained on top with Gomez going close and then Remo Freuler hitting the crossbar.
Gasperini's men continued to push but inevitably the second 45 failed to live up to the brilliant first half.
The margin of victory was well deserved though and Everton already have work to do if they are to progress to the knockout rounds of the Europa League from a competitive Group E.