The Pitmen fell behind on the half hour mark to a fine individual goal from captain Louis Baker.
They remained behind all the way until the 62nd minute when Kyle Rowley headed home from a free-kick.
And from there they turned it around as Andre Landell bundled home with 20 minutes to go, before former Walsall midfielder Reece Flanagan converted a cross from Gibraltar international Reece Styche.
Hednesford had to play out the remaining seven minutes with 10 men after Landell was shown a second yellow card, but they held on to win despite a second goal for Nuneaton in stoppage time.
Stourbridge remain rooted to the bottom of the table after suffering a 1-0 defeat at Stratford Town.
Home goalkeeper Liam O’Brien was in top form in the first half to keep out Montel Gibson and Darryl Knights with a double save. And Stratford took full advantage to lead through James Fry’s 38th-minute header.
Charlie Price kept the Glassboys in the game just after the break with a stunning save from Enoch Andoh, while at the other end former Halesowen Town hitman Gibson saw a shot parried away.
Ben O’Hanlon had a free-kick tipped over in injury time, but that was as close as Stour got and they remain winless this season.
Stafford Rangers slipped to a 1-0 defeat at Hyde United in Northern Premier.
Luke Pilling kept Hyde at bay with a superb save in the first half, but there was nothing he could do to stop Jonah Mitchell giving the home side the win in the 65th minute.
The Boro tried to fight back, with a couple of substitutes going close.
Luca Navarro had a shot saved by the goalkeeper and Tyrone Ofori flicked a Tom Tonks long throw over the crossbar deep into stoppage time.
Halesowen Town’s 100 per cent record came to an end in Northern One Midlands, but a late goal from McKauley Manning at least kept the leaders’ unbeaten start to the season intact.
Paul McCone gave the Yeltz the lead with a deflected header, but fellow high-flyers Carlton Town turned the match around with a goal either side of half-time.
However, with a minute left to play, Manning’s shot hit a defender and went in to send the 610 supporters home with something to be happy about.
Chasetown remain close behind Halesowen in the chasing pack after winning 3-1 at Stamford.
All the goals came in the first half, with the Scholars racing into a 3-0 lead through Aaron Ashford, Jack Langston and Danny O’Callaghan.
Stamford gave themselves a lifeline from the penalty spot on the stroke of half-time, but despite some nervy moments Chasetown held on to win.
Sporting Khalsa continued their decent start to life at step four as they thrashed Bedworth United 4-1.
A deflected shot from Gaz Singh gave Khalsa a half-time lead, but Bedworth levelled not long into the second half. However, Singh, Mason Birch and Jumaane Meggoe quickly restored Sporting’s dominance to wrap up the three points.