Town started the better of the two teams, enjoying a lot of possession and testing the Pro Elite goalkeeper on a couple of occasions.
Despite the early pressure, Town found themselves 2-0 down at the end of the first half.
The second half started like the first with the young Harrogate side pushing for a goal, and the pressure finally paid off when Seb Henry reacted quickest in the box to tap in Oli Bartlett's back post header that cannoned back off the bar.
Not long after, Pro Elite restored their two goal lead from the penalty spot to make the score 3-1.
Town pulled one back when Alex Ingham was set through one on one with the keeper after a brilliant one touch passing move between Tom Hills and Bankole Claudius-Cole.
Entering the last five minutes and after coming close on two occasions, Claudius-Cole grabbed the equaliser after the impressive Pro Elite goalkeeper failed to hold a cross from an attack down the right, tapping in to make it 3-3.
Edward Routh was called into action late on when a long ball caught the town defence out, but Routh was on hand to some how tip a point blank volley onto the bar to secure a draw.