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Goals from Samir Nasri and Sergio Aguero put City two goals up after 47 minutes but Demba Ba’s hooked volley midway through the second period guaranteed a riveting finale.
City held firm to end Chelsea’s notable run of seven consecutive FA Cup Wembley wins, including final triumphs in four of the six previous seasons.
City is building a creditable record of its own in the world’s oldest cup competition and the 2011 winner remains on course to salvage a trophy from what has been an underwhelming campaign.