Following an enthralling 3-3 draw in last week's first leg at the Santiago Bernabeu, a tense and tighter affair was played out in the reverse fixture at the Etihad Stadium on Wednesday night, one in which Los Blancos took a 12th-minute lead through Rodrygo.
The Citizens responded in dominant fashion, boasting 33 shots, 68% possession and 18 corners, but they initially struggled to break down a resilient Real backline. Their persistence in the final third eventually told on the 76-minute mark, though, when Kevin De Bruyne rifled a close-range shot high into the net at the near post.
Real continued to frustrate City in extra time and eventually forced the tie to penalties, and although Luka Modric missed the visitors' first spot kick, City duo Bernardo Silva and Mateo Kovacic both failed to convert from 12 yards to give Real the advantage.
Antonio Rudiger slotted home the decisive penalty to send Real Madrid through to the semi-finals with a 4-3 shootout victory, avenging last season's semi-final loss at the Etihad and sending the Champions League holders packing at the quarter-final stage.
Who asked to be substituted in Real Madrid loss?Before extra time began, Guardiola made the somewhat surprising decision to take off top scorer and first-choice penalty-taker Erling Haaland and replace the Norwegian with Julian Alvarez.
Haaland endured another fairly frustrating night in front of goal; the 23-year-old boasted just 21 touches throughout the 90 minutes, but he did have five attempts of his own, including a towering header that cannoned
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