Atleti were helped by some disastrous defending by Los Blancos, with Dean Huijsen and Eder Militao in particular making a couple of glaring mistakes that cost the visitors goals as they cantered to a 5-2 win at Riyadh Air Metropolitano.
The home side began the match on the front foot, exposing a laxidasical start by Real Madrid, and were deserved leaders when Robin Le Normand opened the scoring in the 14th minute.
The visitors responded well and fought back with a strong showing for the rest of the first half.
Kylian Mbappe levelled the scores in the 25th minute before Arda Gular gave Real the lead 11 minutes later.
However, things went downhill fast for Los Blancos from that point. Alexander Sorloth scored deep into first-half stoppage time to ensure the sides would be deadlocked at the break and the second half belonged to Atleti and Alvarez.
The striker put his side ahead from the penalty spot in the 51st minute before doubling their advantage with his second goal of the game 12 minutes later.
Antoine Griezmann put the cherry on the cake with a lovely goal to hand Atletico Madrid a well-deserved 5-2 win in the Madrid derby.
Elsewhere in LaLiga on Saturday, Girona and Espanyol played out to a 0-0 draw while Alberto Moleiro scored the only goal of the game as Villarreal beat Athletic Club 1-0.
Ivan Romero (26') and Juan Iglesias traded goals as Getafe and Levante drew 1-1 and Takuma Asano scored the winner as Mallorca claimed a 1-0 win over Alaves.
Real Madrid return to La Liga action on Tuesday night looking to end a frustrating run of four games without a win in all competitions when they host Deportivo Alaves at the Santiago Bernabeu.
Pellegrino Matarazzo has hailed Real Sociedad's Copa del Rey victory after they beat Atletico Madrid 4-3 on penalties following a dramatic 2-2 draw after extra time in the final at La Cartuja.
Real Sociedad defeated Atletico Madrid 4-3 on penalties following a 2-2 draw in their Copa del Rey final at the Estadio de La Cartuja in Seville on Saturday.
Antoine Griezmann has admitted he is feeling the weight of the moment ahead of today's Copa del Rey Final, as Atletico Madrid prepare to face Real Sociedad - the club where his career first took off.
