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The striker, who scored the winner against Blackpool at the weekend poped up to score a last gasp winner and give City a chance of facing one of fourteen Premiership clubs in the next round.
Peterborough, who were slightly harshly done by having led for most of the game, scored early on through George Boyd before Louis Carey equalised for the home side just after half time.
The game was balanced on a knife edge but City snatched it when Joe Lewis saved from Michael McIndoe but Brooker was on hand to tap home the winner.
A full match report will appear on the site later.