But Real grabbed a vital away goal when Isco poked in a rebound after Toni Kroos' fierce shot - following a brilliant run by Karim Benzema - was saved.
It checked Atletico's momentum and left them needing three more goals to reach a third Champions League final in four seasons.
Chances were scarcer for both teams after the break, although home substitute Kevin Gameiro missed two presentable chances to give Atletico a glimmer of hope.
Ultimately, the damage from the first leg was irreversible as Real beat their neighbours in the competition for the fourth successive season.
Zinedine Zidane's team, attempting to become the first team to win the Champions League twice in a row, will meet Juventus at the Principality Stadium on Saturday, 3 June.
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Relive an enthralling Madrid derby
Too little, too late for Atletico
Most people thought this tie was a foregone conclusion after Atletico were outclassed at the Bernabeu eight days ago.
Los Rojiblancos, who managed just one shot on target in a limp away performance, had other ideas.
Knowing they needed at least three goals to stand any chance of progressing, Diego Simeone's side tore out of the blocks in the opening 20 minutes.
Atletico hassled and harried the visitors, creating gaps in a panicky away defence.
Real keeper Keylor Navas had already saved from Koke inside the opening five minutes before the Atletico midfielder swung in a right-wing corner which Saul met at the near post to powerfully head in.
The visitors had not conceded twice inside the opening 20 minutes of a Champions League match since 2004 - but Griezmann ended that record after Fernando Torres was bundled over by Raphael Varane's clumsy tackle.
Griezmann missed a penalty against Real in last year's Champions League final, as well as two more spot-kicks in La Liga this season, but his Paneka-style chip sneaked past the diving Navas.
La Liga leaders Real looked flustered as the noise was ramped up by the home supporters.
However, they knew one away goal would completely change the complexion of a compelling match - and Isco's opportunist strike did exactly that.
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