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It looked like a practice game at times for Pep Guardiola's side at Hillsborough but they struggled to convert their overwhelming superiority into goals.
Nicolas Otamendi and Benjamin Mendy were both denied by the woodwork before Aguero finally made the breakthrough in the 53rd minute courtesy of an error by keeper Joe Wildsmith.
Leicester City beat Birmingham City 1-0 to book their place in the last eight -- Ricardo Pereira's late header sealing a tight Midlands derby.
Tottenham Hotspur and Norwich City were playing extra time after their fifth-round tie ended 1-1.