Looking to overturn defeat in the first leg, the Serie A club were undone by a goalkeeping howler from Marco Sportiello to allow Karim Benzema an easy finish midway through the first half.
The Orobici saw hopes of a comeback were extinguished when Sergio Ramos scored a penalty on the hour mark after Vinicius Junior was caught. Although Luis Muriel netted a late consolation with a superb freekick, his strike was immediately cancelled out by a Marco Asensio goal.
Atalanta started on the front foot and almost levelled the tie in the opening minutes as Robin Gosens met a low Muriel cross from close range, but couldn’t connect well enough to test Thibaut Courtois.
La Dea were enjoying the better of the play but it was Real Madrid who had the best chance for the opener. A quick break saw Vinicius race into the area and play a one-two with Benzema, but his effort was blocked by Berat Djimsiti.
The hosts almost made a dream start to the second half as Vinicius dribbled from the halfway line to dance through the Atalanta defence and into the box but could only drag his shot wide.
Vinicius effectively wrapped the tie up on the hour mark as he stole possession and charged into the area, with Toloi clipping him and conceding a penalty. Ramos stepped up and drilled his spot kick in, despite Sportiello getting a hand to the shot, to extend Real Madrid’s advantage further.
Atalanta finally tested Courtois through a powerful Duvan Zapata strike but the hosts almost scored again, with Benzema seeing a close-range header palmed out by Sportiello before his follow up came back off the post.
La Dea’s best chance came late on as Zapata met a well-weighted Ruslan Malinovskyi pass to get in behind, but was denied by the outstretched leg of Courtois.
The visitors enjoyed an impressive last quarter of an hour and reduced the deficit late on as Muriel rifled in a wonderful freekick. However, only for Real Madrid hit back immediately through Asensio to seal a comfortable victory.