The Lilywhites produced their most impressive display of the season when they dismantled an impressive and occasionally dangerous Hednesford team in a match which they dominated for long stretches.
The continued absence of James Krause meant that manager Gary Roberts retained the starting eleven that drew 3-3 with Salisbury at the weekend, Joey Abbs securing his spot at left back.
The opening exchange were a little tentative as both sides found their feet, but soon a pattern emerged with City showing the greater fluency and urgency. When David Kolodynski hit the bye-line and wriggled his way towards goal it took a timely intervention from Scott Fuller to prevent his pass finding Craig Hammond.
Kolodynski once again showed his movement and mobility when he nearly sprang the offside trap only to be flagged by the assistant referee on ten minutes and when Adrian Cambridges overhead kick put in Hammond seconds later, it was again the flag that saved the Pitmen.
City continued to have much the better of the opening quarter and when Tony Burke shimmed through the home defence on 13 minutes he looked odds on to score, only to be denied by an excellent save from keeper Dan Crane.
Hednesford, however, also had the ability to hurt City, especially via the dangerous Mark Bellingham. However, City's back four were in good form, never better than when Dave Theobald made a timely interception on 31 minutes to snuff out a telling through-ball. Other than that, the defence kept Hednesford at bay, Barrett not being worked particularly hard in the first half.
But it was City who were creating the better chances. Two penalty shouts for handball went unheeded, referee Barrow being given no support from his assistant. One looked speculative, the second much stronger. However, the Lilywhites continued to create chances and on 25 minutes Kolodynski tried his luck from 20 yards with a dipping drive that skimmed the bar when he might have done better to put in Hammond.
The visitors ended the half well, but with no goals to show for their efforts.
When the Pitmen came out for the second half it was with real intent. For ten minutes they looked the sharper team and one sensed that if they were going to score it would be now. But City absorbed the pressure and gradually found their feet again and Hednesfords moment had passed.
The Lilywhites finally made it on to the score sheet on the hour when John Kennedys cross found Hammond, who had his first effort half saved by Crane but was quick enough to respond first to bundle the ball home to give City a vital lead.
It looked certain that Kolodynski would open his account soon after when he found himself in space on the edge of the box with time to pick his spot, but somehow lofted the ball high over the bar. The striker did better seconds later when he drew an excellent save from Crane who had to dive at full stretch to keep his shot out.
Although City were dominating, their lead was slender and Mark Bellingham was always likely to pop up and cause a problem. He tried a curling shot on 70 but apart from that, was kept quiet until the closing moments of the game.
Meanwhile, Kolodynski finally made his personal breakthrough on 71 minutes when he took what was a difficult chance, smashing the ball past Crane at a tightest angle to give his side a welcome two goal lead.
City were in an almost identical position at the weekend and knew that the Pitmen would throw everything they had at them. Sean Platt blasted over when he should have tested Barrett, who just minutes later earned his money with a fine save that retained his sides cushion.
Right at the death, Bellingham hit the post with a header, but City held on, kept their nerve and took a very well deserved three points with a performance that was full of endeavour and spark.
Make no mistake, Hednesford are a very decent outfit who will win many games this year. Their pitch is excellent, as is their stadium. And how nice to be welcomed with smiles and thoughtfulness by officials and fans alike.
Hats off to the City hardcore who made the trip too. A small but discerning group shouting the lads on all night. A fine effort.