Cole Palmer put the blues one goal up in the 16th minute.
Harry Wilson later equalised for the visitors in the 82nd minute, and Rodrigo Muniz slotted home the winner in stoppage time.
Elsewhere AFC Wimbledon were held to a 1-all draw by Swindon Town at the Cherry Red Records Stadium.
The visitors went a goal ahead when Harry Smith scored in the 10th minute.
Wimbledon’s equaliser then came in the form of James Tilley in the second half.
Speaking before the game, Manager Johnnie Jackson was feeling confident going into the new year, despite a spate of injuries.
