Koji Miyoshi earned Birmingham a last-gasp victory after a five-man substitution paid off for manager Tony Mowbray.
Birmingham had to battle back from a goal down to seal a fourth round tie at Leicester City.
It earned Mowbray his first victory as the club’s manager after taking over last week.
But Jason Lokilo’s first goal for Hull opened the scoring after 12 minutes.
Birmingham pressed for an equaliser, but Mowbray’s decision to change half his outfield players swung the game his side’s way.
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