The capital club were not at their best, but can now look forward to facing Barcelona in the final.
Despite failing to inspire for long spells of the match, Mesut Oezil's sublime finish with ten minutes to go put paid to the challenge of the ineffective visitors, and then Emmanuel Adebayor's injury-time volley set up a final meeting of Spain's two biggest sides.
Sevilla knew that they had to find the net or else face elimination, and opted to play Frederic Kanoute just off main striker Alvaro Negredo, fresh from his two goals at the weekend.
But it was Madrid who created the better chances in the first half. Angel Di Maria cut inside from the left flank after just four minutes, drilling in a low shot that cannoned back from the base of the post. Karim Benzema looked destined to slot home into the empty net, with Javi Varas stranded, but his effort skewed wide of the target.
Negredo had a goal chopped off for a borderline offside decision before Cristiano Ronaldo squandered the best chance of the opening 45 minutes. Di Maria slipped him through on goal, but as the ball ran across his body, Varas blocked his low effort well with his legs.
Neither side were wholly convincing, however, and Sevilla, while holding their own, weren’t doing enough to press for the goal they were required to seek.
Madrid were wasteful once more. Di Maria forced Varas into another good save with his lower body, then Ronaldo’s bobbling cross was headed over from underneath the crossbar by the hapless Benzema.
Luis Fabiano was thrown into the action by away coach Gregorio Manzano, but their build-up play remained ineffectual, and they lacked the belief to truly press for a goal that would take the match to extra time.
And they would be made to pay for their lack of vibrancy when los Blancos killed the contest. A quite brilliant through pass from Sami Khedira bisected the Nervionenses' back four and international team-mate Oezil conveyed immense composure to feign Javi Varas, dance around him and roll the ball into the net.
Icing was added in the final minute when Adebayor, given the last ten minutes of the match, controlled a Diarra pass on his chest before lashing home an unstoppable volley into the roof of the net.
The late goals gloss over what was an unconvincing Madrid performance, but they did the necessary to progress, dethroning the holders to establish the first Clasico cup final since 1990.