Iran Press/ Europe: City traveled to the Spanish capital as favorites after winning the first leg 4-3 in Manchester eight days earlier.
City fans will have been frantically booking flights to Paris as their side led 1-0 on the night and 5-3 on aggregate with 40 seconds of normal time remaining.
Real had not even mustered a shot on target by this point but then came two minutes of mayhem as substitute Rodrygo scored twice to force extra time.
Karim Benzema then converted a penalty in extra time to send Real through to their 17th European Cup final, where they will face Liverpool on May 28.
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Benzema extra-time goal sends Real to semis