The equaliser came on 67 minutes when Williams fizzed a low free-kick straight in to the far corner from the left of the penalty area and the Yellows pressed for a winner.
Jamie McDonald was introduced as a substitute to make his second debut for the club and within five minutes he had warmed the fingertips of Hawkins after Williams had released him in the left channel.
The best chance fell to Duggan, who forced the save of the match from Hawkins to deny the defender’s header from Duffy’s deep cross.
A draw was probably the end result – but a greater concern for the Yellows will now be the future of their manager.
They are next in action on Saturday against Morpeth Town in the FA Trophy.
Mickleover: Hawkins, Bennett, Gough, Butler, Watt, Agustien, Bateman, Warren, Arnott (Dales), Beavon, Walters (Davidson-Millar). Unused subs: Mann, Mills, Lee.
Warrington Town: Atherton, Baillie, Regan, Williams, Roberts, Duggan, Grivosti (Mackreth), Mols, Reid (J McDonald), Dixon, Duffy. Unused subs: Gumbs, M McDonald