Things had looked rosy after 25 seconds of Saturday's League Two clash at the Recreation Ground when Chester were awarded a penalty after 18-year-old Lee Ellans was bundled over by Shots skipper Ricky Newman.
Top-scorer Ryan Lowe lashed home on the rebound after Nikki Bull saved his original attempt.
But Aldershot hit back after 15 minutes when Hudson beat the Blues' offside trap and spectacularly lobbed Chester's emergency loan signing Jamie Spencer.
Hudson started where he left off 11 minutes after the break smashing another vicious volley past Spencer.
But Chester controversially drew level in the 63rd minute. Lowe diverted James Vaughan's shot goalwards and despite home keeper Bull lying injured on the ground trainee Ellans fired home for City, who now require a 20-goal swing to beat the drop to the Blue Square Premier.