Chris Wood's hat-trick earned victory for Leicester as four goals in 16 minutes cut Carlisle apart in their second-round Capital One tie.
League One Carlisle took an early lead through David Amoo's low shot.
But Wood levelled before the break from Anthony Knockaert's pass before Lloyd Dyer finished after a clear run.
Championship Leicester added a third via Knockaert, with Wood's penalty and a cool strike completing his treble before James Berrett curled in.
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