The City second string were at Oakwell to take on Barnsley, and the home side went ahead on 73 minutes after threatening to score for most of the match.
However, Simon Johnson followed Leo Bertos' strike with an equaliser minutes later.
But a minute later Jeremy Christie restored the Tykes' lead to win them the game at 2-1 and take them through to the next round.
However, Simon Johnson followed Leo Bertos' strike with an equaliser minutes later.
But a minute later Jeremy Christie restored the Tykes' lead to win them the game at 2-1 and take them through to the next round.