A turgid first half was brightened only briefly when Asfordby snatched the lead.
Bullimore’s cracking volley rocked the crossbar and Crowther clinically dispatched the rebound.
After the break, sloppy defending allowed the hosts to equalise with a soft shot before Asfordby squandered several good chances from precision corners from Thompson and Brown during a spell of sustained pressure.
Partridge made a great goal-line clearance, but Asfordby’s earlier profligacy was punished when a bizarre error at the back put Houghton ahead.
The visitors responded tremendously with two quick goals. Harrison levelled with a sublime volley before Shirtcliffe’s deft header from Crowther’s cross put them 3-2 ahead.
But with just a few minutes left another lapse in concentration gifted Houghton an undeserved equaliser.
Asfordby: S. Davies, D. Exton, M. Shirtcliffe, J. Partridge, J. Scatchard, W. Knatt, E. Harrison, E. Thompson, A. Brown, K. Doody, S. Bullimore.