Honours were even after the two previous encounters away from home.
Stratford were in 18th place prior to kick-off having played three more games than fifth-placed Hednesford.
The Town had not won in the league since the 4-1 win against the Pitmen in November.
With heavy rain all week and many postponements elsewhere ground staff David and Val Bates were the pre-match heroes getting the surface ready.
Ahead of the game joint caretaker manager Danny Glover said: "We have played at Stratford twice and we know it will be another tough game. Although we beat them 2-1 in the FA Trophy, they got the better of us in the league. The lads will be well prepared and ready to go; hopefully we will put it right."
The Pitmen created a flurry of early opportunities starting with a Reece King's header from the edge of the box forcing a save from Sam Lomax.
Elliot Hodge saw his goal bound effort, blocked on the line with James Hurst putting the rebound just wide.
Izak Reid put in a dangerous cross from the right for Osebi Abadaki to force another save from Lomax, with Danny Glover's effort from the rebound going behind for a corner.
The early pressure continued when Glover flashed a cross wide with Reid just inches short of tapping the ball in.
The visitors seemed happy to soak up the pressure and try to hit the Pitmen on the break with long balls up towards lone striker Chris Wreh.
Despite having the vast majority of the possession the Pitmen were unable to break the deadlock in the first half.
The second half started with the visitors creating their best chance of the game when Lewis Wilson produced a dangerous cross from the right which Tom Mehew put over the bar from close range.
The game then reverted to the same pattern as the first half with the Pitmen buzzing around the Stratford half, maintaining most of the ball without creating too many clear cut chances.
Reid's header forced a save from Lomax while Hurst saw a long range attempt sail over the bar.
Just before the hour a hefty challenge from Reece King on Wilson saw the visitors call for a dismissal, however the referee opted to book the Pitmen midfielder.
A long ball from Andy Wycherley was controlled by Glover whose sharp volley went inches over.
The break through came as a decisive run by Abadaki was ended as Lomax hauled him down in the Stratford area, Danny Glover stepped up to dispatch the penalty kick low to the keeper's right in the 70th minute.
Andy Wycherley had to tip the ball over the bar as the Pitmen defended a corner late on but remained in control of the game.
Glover had the chance to put the result beyond doubt after breaking down the right wing before cutting in and sending a shot just wide of the far post.
The Pitmen hung on for a well-deserved win in a game that they controlled from start to finish.
Hednesford Town; Wycherley, Curley, Griffiths, Bailey (C), Morris (Gatter 64), Hurst, Hodge, King, Glover, Reid, (jones 76) Abadaki. Subs not used; Fry, Hallahan, Veiga.
Stratford Town; Lomax, Vann, Woolard-Innocent (Ambris 86), Richards, Bower, Rowley, Wilson (C), Nabay, Wreh, Mehew (Clement 86), Davidson (Campbell-Mhlope 78). Subs not used; Bennett, Atkins