The squad was boosted by the return to fitness of Courtney Richards and the the arrival of forward Chay Tilt as the Pitmen sought to extend their unbeaten start to the season.
Cleethorpes Town have started their league campaign in the Northern League East reasonably well, currently sitting in eighth place, despite being a league below the Pitmen, the Owls triumphed in the last meeting between the two sides, winning an cup replay after a 1-1 stalemate at Keys Park.
The Pitmen got off to a strong start, dominating the opening stages of the game and it was no suprise when Andre Landell opened the scoring in the 12th minute heading home debutant Chay Tilt's inviting cross.
Minutes later Tilt could have extended the Pitmen's lead when he got on the end of Carter Lycett's left wing cross, Owl's keeper making the vital save with his feet.
There was a hint of offside when Josh Batty had a great chance to equalise when through on goal but his tame shot was easily saved by Andy Wycherley.
A flat second half performance from the home side failed to kill off the tie as Cleethorpes battled their way at back into the game. Substitute Josh Smaller had only been on the pitch for a minute when he rose above everyone else to head Cleethorpes Town level in the 72nd minute. Both sides fought for a breakthrough to settle the tie, but in reality there were no more clear cut chances setting up a replay on Tuesday night.
Hednesford Town; Wycherley, Webb, Pryce (Griffiths 54), Bailey (Richards 46), Rowley, Ison, Tilt, Parker, Brown, Landell (Chambers 64), Lycett. Subs not used Morley, Wollaston, Hanna
Cleethorpes Town; Jackson, Walker, McKay, Topliss, Cooke, Donald, Dickens, Flett, Batty (Smaller 71) Robertson, Venney. Subs not used, Boswell, Lowe, Middleton