Saul and Griezmann gave the hosts hope of a comeback before Isco's away goal ensured Real will face Juventus in Cardiff.
A breathless, ferocious, compelling 90 minutes only served to deliver the same old ending in a fitting European goodbye to the Vicente Calderon.
Atletico Madrid threw everything at ending their Champions League curse against their nearest and dearest rivals, but it is Real who march onto the final once more.
For 42 minutes the impossible dream seemed on.
Saul Niguez powered home Koke's corner before Antoine Griezmann ended his penalty jinx against Real after Raphael Varane had upended Fernando Torres.
Atletico charged into every tackle, strained every sinew, but ultimately left themselves far too much to do in losing last week's first leg 3-0.
That much was confirmed when Real's standout player on the night Isco pounced three minutes before half-time to tap home after sensational skill from Karim Benzema in the build-up.
A Real away goal left Atletico needing five, which they never threatened to get even if a first victory over Real in four attempts this season did slightly ease their pain.
In its 50 years of history it is hard to imagine the Vicente Calderon has seen a night like this.
The special cauldron of an atmosphere that has swept aside Barcelona and Bayern Munich twice here in recent seasons was cranked up a few notches for the one European scalp still to allude Atletico.
Having lost out to Real in the Champions League for the past three years via a series of late goals and a penalty shootout, it was no surprise Atletico got so close before having their hearts broken once more.