The former Liverpool and Chelsea striker scored his first two goals since rejoining his boyhood club as Atleti claimed a 2-2 draw at the Bernabeu to reach the last eight of the competition thanks to a 4-2 aggregate success.
Torres found the net in the first minute of each half to end any hopes of a fightback from the reigning world and European club champions.
Real replied to each goal with equalisers from Sergio Ramos and Cristiano Ronaldo but it was not enough for the La Liga leaders.
Torres immediately punctured what had been a vibrant atmosphere, fuelled by Ronaldo’s parading of the Ballon d’Or trophy before kick-off, by sweeping home Antoine Griezmann’s cross with less than a minute gone.
Real responded well, with Ronaldo denied at close range before Ramos planted a firm header past Jan Oblak.
Ronaldo had another effort blocked and also headed wide from a Gareth Bale cross as Atleti were extended at the back.
Real might have looked to step up further after the break but again they were stung within a minute of kick-off as Ramos gifted possession to Griezmann who quickly fed Torres, who wrongfooted Pepe and finished coolly, albeit with a helpful deflection off keeper Keylor Navas.
Again Real responded, Ronaldo heading home Bale’s cross eight minutes later, but the task was beyond Carlo Ancelotti’s men, who have not beaten Atleti in five attempts since last season’s Champions League final.
Barcelona, beaten by Real in last year’s final, will face Atleti in the??quarter-finals next week after wrapping up a 9-0 aggregate win over La Liga??strugglers Elche.
With a five-goal advantage from the first leg, the Catalan giants made 11??changes at the Estadio Martinez Valero, resting the likes of Lionel Messi,??Neymar and Luis Suarez.
They hardly needed their stars and went ahead with a superb free-kick from??Jeremy Mathieu after 21 minutes.
Sergi Roberto added the second with a fine left-footed strike from outside the??area and Pedro’s penalty, after Munir El Haddadi was fouled, made it 3-0 on the??stroke of half-time.
Barca eased off in the second half but highly-rated teenager Alen Halilovic??came off the bench to make an eye-catching debut in which he curled a shot??against the post.
Adriano completed the scoring with a firm header in injury time.