The result on the night was enough to give Madrid a 5-2 aggregate victory against their fellow Spaniards.
The hosts were dominant in the first half, but were denied on numerous occasions by an inspired Thibaut Courtois in the Atletico goal.
However, Diego Simeone's side put the game beyond doubt just after the hour when Adrian Lopez fired in on the angle from Diego Ribas's incisive pass.
They almost doubled their lead soon after, but Radamel Falcao's effort was saved by the feet of Diego Alves.
Atletico's night was soured with 10 minutes to play when Tiago was shown a straight red card for slapping Roberto Soldado around the face during a spat between the two sets of players.
Madrid will now meet Athletic Bilbao in an all-Spanish final in Bucharest on Wednesday, May 9.