Substitute Jim Thwaites equalised in stoppage time with a stunning strike, after Derby captain Luke Banks looked to have given the hosts three points with a towering header midway through the second half.
Jack Kingdon volleyed home to level for United in the first half, after Cruz Allen's low strike put the Rams ahead after three minutes.
Adam Lawrence's team may have dropped points for the first time this season but it was another useful learning experience for his young Reds against a competitive opponent.
United suffered an early setback at Moor Farm when Allen fired a low left-footed shot into the bottom corner from around 22 yards to put the hosts ahead in the third minute.