Atlético won on the night, in their last-ever European game at the Vicente Calderón, but it was Real Madrid who marched on to the final against Juventus in Cardiff on 3 June.
The Zinedine Zidane team will now attempt to become the first side to successfully defend their UEFA Champions League crown.
The qualification tonight was nearly impossible.
Atlético required a minor miracle after last week’s Cristiano Ronaldo-inspired 3-0 first-leg defeat but amid a sensational opening their prayers looked like being answered.
Saúl Ñíguez’s header raised hopes and when Antoine Griezmann’s mis-hit penalty found the net four minutes later, it was on.
In a semi-final played at frenetic pace, Zinédine Zidane’s men slowly found their poise and three minutes before half-time the white half of the Spanish capital breathed a collective sigh of relief as Isco slotted in.
It meant Atletico had to score three more; to their credit, they gave it a go.
Yet when Kaylor Navas brilliantly denied substitute Kevin Gameiro midway through the second period, the jig was up.