Stockport almost equalised immediately but Dean Bouzanis in the Liverpool goal was playing well and kept the Hatters attack at bay with some good saves.
Liverpool almost went 2-0 up early in the second half after Jordy Brouwer and Bruna combined to send the Argentinian through but his shot was saved by the keeper.
That was the wake up call Stockport needed and they finally equalised just after the hour mark.
Brouwer and subsitute Nathan Ecclestone had late chances to win it for the Reds but were denied by the keeper as the game finished all square.