Diego Simeone's side, who sit alongside Barcelona at the top of the Primera Division, took just 13 minutes to open the scoring through Raul Garcia and went from strength to strength.
Arda Turan added a second after 20 minutes and scored again 10 minutes into the second half, before substitute David Villa rounded off the win six minutes from time.
Things did not go to plan for city rivals Real Madrid, however, as they failed to break down a stubborn Olimpic Xativa side and had to settle for a goalless draw against the Segunda B outfit.
Celta Vigo gained the edge in their all-Primera Division clash at home to Athletic Bilbao, with Santi Mina scoring the only goal after 71 minutes in a 1-0 victory.
Top-flight Getafe will take a 1-1 draw into the second leg of their clash with Segunda Division side Girona.
The home side led after 16 minutes through David Timor but Getafe were level seven minutes before the interval thanks to Ciprian Marica.
Another La Liga side, Levante, succumbed to a last-minute goal from Ruyman Hernandez as they were edged out 1-0 by Recreativo Huelva.
The return legs will be played between December 17 and 19.