Atletico led 2-0 from the first leg and Torres stunned the Bernabeu, smashing in left-footed after 49 seconds.
Sergio Ramos's header levelled but, in the first minute of the second half, Torres beat Pepe to slide in a second.
Real needed three goals to win after Cristiano Ronaldo's header but Atleti will meet Barcelona in the last eight.
Barca cruised to a 9-0 aggregate win over Elche, but for Atleti, the last-16 stage provided a stiffer test and significant bragging rights.
The La Liga champions inflicted a first domestic cup defeat on Carlo Ancelotti since he arrived to manage their city rivals in 2013.
Los Rojiblancos can also boast being five games unbeaten against Real this season, a record which looked certain to continue after less than a minute's play in the Spanish capital.
Soon after Ronaldo stopped parading his Fifa Ballon d'Or award moments before kick-off, Torres plundered the opener, sweeping into the top corner from 10 yards with a first-time shot following Antoine Griezmann's cross.
Torres, who left Atleti in 2007, had never scored at the Bernabeu with his boyhood club but, in for the unwell Mario Mandzukic, he left Real needing four goals to progress.
Ramos netted a last-minute leveller which spurred Real on to a 4-1 extra-time win over Atletico in last season's Champions League final and he was in the right place when goalkeeper Jan Oblak - making just his fifth appearance - flapped at a set-piece delivery.
Media playback is not supported on this device
Swarms of white shirts peppered the visitors' area and Ronaldo's goal-bound strike was only kept out by Mario Suarez on the goal-line as Real dominated with 76% of possession in the opening half.
But Diego Simeone's side only had 27% of the ball in the first leg and they again demonstrated the resilience he has instilled in them since taking over in December 2011.
The Argentine has delivered successive league finishes of fifth, third and first along with Europa League success in 2012 and a Copa del Rey triumph in 2013.
In Europa League, Champions League and Copa del Rey fixtures, he now has 16 successes from 18 two-legged ties and Torres's second came at the perfect time, killing Real's second-half hope.
He again collected a Griezmann pass before wrong-footing Pepe to fire under home keeper Keylor Navas.
Ronaldo - voted the greatest player in Portugal's history on Wednesday - headed in from six yards to reduce the arrears on 54 minutes before Torres was substituted to jeers from the home fans.
Karim Benzema could not turn their frustration to hope when he fired over from four yards as La Liga leaders Real relinquished their hold on Spain's coveted domestic cup.
What is a summary of this text?
Fernando Torres struck his first goals since returning to Atletico Madrid, firing a brace in a 4-2 Copa del Rey aggregate win over holders Real Madrid.