Atletico came into the encounter full of confidence after going three points clear at the top of the Liga table at the weekend, but they were no match for their neighbours in Wednesday's semi-final first leg.
It did not take Real long to forge ahead, as a Pepe's effort struck Emiliano Insua and flew past Thibaut Courtois after 17 minutes, delighting the home fans.
Pepe endured a bruising duel with Atletico's Diego Costa throughout the first half, but the defender came out on top and Real managed to double their lead in the second half when Jese Rodriguez placed a clever finish under the goalkeeper.
The hosts wrapped up the win and went a long way to securing their final berth as Angel di Maria saw his long-range effort deflect off Miranda before beating Courtois with 17 minutes left.
Defeat for Atletico ended their unbeaten run in all competitions at 23 matches, while Real have now not lost for the same number of games.
Despite being declared fit on Tuesday, Gareth Bale missed out for the hosts with a calf strain, while Atletico were unable to call upon David Villa – suffering from a hamstring problem.
Diego Simeone’s men looked nervous at the back in the opening stages, but the match’s first opportunity fell to them as Arda Turan met Juanfran’s cross near the penalty spot, only for Iker Casillas to parry the Turk's header away.
Real made the most of that let-off as Pepe helped to open the scoring in the 17th minute, the Portugal international’s shot from 25 yards taking a wicked deflection of Insua before flying past the helpless Courtois.
After a hotly contested first half-hour, Atletico's Belgian goalkeeper then denied Real a second goal twice in quick succession in the 32nd minute. First, Jese cut in from the left and stung Courtois' palms with a driven effort, before Luka Modric hit a volley straight at him from the edge of the area.
Carlo Ancelotti's men exerted some pressure again at the start of the second half and Cristiano Ronaldo tried his luck after running at Juanfran, but his low shot was saved by Courtois, who continued to keep Atletico in the contest.
The shot-stopper's luck ran out eventually, however. Di Maria's delicate pass with the outside of his left foot dissected the visitors' defence with 57 minutes played and Jese squeezed the ball under the goalkeeper with a deft flick.
Di Maria was involved again in Real's next attack, as his 30-yard effort was saved nervously by Courtois, before a tackle from the Argentinian drew a petulant reaction from Diego Costa, earning the forward a yellow card - which rules him out of the second leg.
Real completed the victory in the 73rd minute as Miranda deflected Di Maria's 30-yard strike past Courtois, putting last year's runners-up a giant step closer to sealing a final place.
