It was an exhilarating opening fifteen minutes, and both sides could easily have opened the scoring.
In the very first minute, hesitancy in the Blues defence allowed Michael Bowler an opening, and his firm low shot had to be brilliantly turned away by an alert Chris Thompson.
Just a minute later, Nelson's Lance Ogunyode played a delightful through ball to Sam Heap, who was forced wide by the keeper. He then curled a shot back towards goal, but saw his effort cleared off the line.
On four minutes a slack clearance from the Blues back line presented New Mills captain Carlos Meakin with a chance, and Nelson were relieved to see his shot take a slight deflection as it flew wide of the left hand upright.
Three minutes later Ashley Williams failed to trouble the home keeper with a low shot, and in Nelson's next attack a long punt forward from Thompson was headed on by Sam Heap to release Ashley Higgins. The keeper blocked his first effort, but Higgins then screwed wide from a better second opportunity.
Ten minutes in a New Mills free-kick from the left was headed back across goal into the danger area, with Cayne Hanley putting a great chance wide. And on the quarter hour a long jinking run from Matty Taylor ended with a drilled shot which Thompson smartly got down to parry.
The game then settled down a little, but New Mills took the lead on the half hour in their next meaningful attack. Taylor looped the ball in from the right, and a simple touch back inside left captain Meakin in acres of space around the penalty spot to pick his spot, and he did, giving Thompson no chance as he smashed the ball into the left of the net.
With five minutes to go to half-time Nelson carved out another effort. Higgins cut inside well after receiving the ball on the right, but his low shot didn't have the power to trouble the keeper.
But with Nelson looking to get to half-time just one goal down, and ready to benefit from the slope in the second half, the home side grabbed a second. It looked like a foul on a Nelson player as a long punt was flicked on, but the referee allowed play to continue, with Hanley taking advantage to run onto the loose ball and drill it past Thompson.
It almost got worse for Nelson before the break when a cross to the right hand side was headed back across for Mark Innes, and only a brilliant reflex save from Thompson prevented a goal, with Innes then hitting the outside of the post from a tight angle from the resultant loose ball.
The second half started slowly, and the first real chance came on 56 minutes as Meakin played in Mark Cadwallader, who forced a save from Thompson. Cadwallader then nipped in for the loose ball and found Meakin, who headed wide from a narrow angle.
Midway through the half Meakin tested Thompson again with a low free-kick, and soon after some slack defending allowed Hanley to turn smartly and fire narrowly wide of Thompson's right hand upright.
With twenty minutes left, Nelson created their first real opening of the second half, when a smart ball from Daniel Finch played in Heap, whose shot as he burst into the area was well blocked.
With 13 minutes left, home captain Meakin laid a simple ball into substitute Andrew Smith, and Thompson was again called upon to make a smart save low to his left at the expense of a corner.
Higgins went on a mazy run for Nelson with nine minutes remaining, but with better options around him ended up hitting a weak shot straight at the keeper.
And in the final minute of a strangely long injury time, New Mills wrapped things up with their third. A free kick from wide out on the left found the unmarked Garry Kharas six yards out, and he had the simplest of tasks to nod home into the bottom left hand corner.
The Blues' attentions now turn to the cups, with a trip to Ramsbottom on Tuesday in the LFA Trophy followed by a home match against NCE side Selby Town in the first round of the Vase next Saturday.