Warburton's free-kick gave Town a half-time lead, after which Halifax only got better in a performance full of heart and spirit, against a County side seemingly devoid of both.
Bradbury's second goal in two games and Waters' sixth of the season sealed a memorable victory and rounded off a fantastic week for Town after four points against Southend and Boreham Wood.
The Shaymen got better as the game went on, surviving moments when they had to before simply overpowering their opponents through force of will and determination.
And The Shay crowded, bathed in September sunshine, loved it.
Stockport tried to create pretty patterns with short, sharp passing, and were aggressive out of possession, wanting the ball back as soon as they lost it.
As a result, Town needed to attack at pace, and make the most of what possession they got.
County's slight superiority early on was exemplified when John Rooney ghosted past three Town players on the edge of their box and then curled a lovely shot off the post.
Niall Maher was busy from the off, clearing passes into Town territory, while Halifax's lack of composure on the ball was just handing it straight back to the visitors.
Kian Spence made his first start of the season in place of the rested Martin Woods - big shoes to fill after Woods' superb form - while Jack Senior returned after injury.
But neither got much opportunity to demonstrate their attacking capabilities as Town were made to work hard to stay level.
Rooney and Will Collar were never far from Spence and Kieran Green in middle of the pitch, making it difficult for the hosts to find the breathing space to operate.
County, and Rooney in particular, controlled and moved the ball extremely well, but couldn't turn their stronger start into clear chances.
The Shaymen looked less likely to score than the visitors, and didn't get as close to doing so as, like last season's fixture at The Shay, County defended effectively, giving nothing away.
Halifax nearly gave away an own goal when Alex Reid's low cross was diverted onto the bar and over by Maher in what turned out to be a very good interception, but only just.
How's your luck Niall? Last season his error led to Stockport's winner here, this season, things seemed to be going Halifax's way.
And when former Town man Liam Hogan was booked for wiping out Warburton just outside the County box - the first time the visitors' defence had really looked stretched - the former Stockport attacker struck a superb low effort into the far corner from 20 yards.
After another example of the former player curse striking again in midweek through Scott Boden, how nice it was that another club was on the receiving end.
On the balance of play, Stockport might have wondered how they were behind, but Sam Johnson - on his 250th appearance for Town - hadn't been tested by half-time, emphasising that for all County's urgency, there had been little end-product. Halifax had one shot, and scored from it.
Things didn't bode well for Stockport minutes after the interval when Town's high press led to a chance for Waters, but his tame effort was comfortably saved.
Halifax were snappier after half-time, biting into tackles more and not inviting pressure as much, typified by the typically energetic Green in the engine room. It also helped that Stockport hadn't got going since the restart, and looked decidedly flat.
Keeper Ben Hinchliffe kept out Jordan Slew's effort after Town had again pressed high to good effect, before an error by Ben Barclay allowed Billy Waters in one-on-one at an angle, but his chip went wide of the near post.
Stockport manager Simon Rusk had seen enough, and a couple of changes saw them switch to a back four. But the visitors had to match Town's hunger and desire.
Johnson was finally tested midway through the second-half when he did brilliantly tip over Rooney's terrific effort across goal.
A great block by Macauley Southam-Hales kept out Warburton's effort amid a burst of Town pressure.
Despite their changes, County still weren't creating enough, while Town were now a much stronger attacking force and growing in confidence, with Slew making inroads down the right, and his lovely one-two with substitute Jamie Allen preceded a low cross from the left that Bradbury converted from close range.
Stockport had slunk into a pale imitation of the title-challengers they were expected to be before the season a while before Bradbury's goal, and there was no way back after it, with Town in the ascendancy, full of passion and purpose.
Waters added the gloss in added time with a cool finish past Hinchliffe from Warburton's through ball.
Halifax: Town team - Johnson, Warren, Maher, Bradbury, Senior, Spence (Woods 77), Green, Slew (Tear 90), Warburton, Gilmour (Allen 60), Waters. Subs not used: McDonagh, Swaby-Neavin.
Scorers: Warburton (42), Bradbury (78), Waters (90)
Shots on target: 4
Shots off target: 6
Stockport: Hinchliffe, Southam-Hales, Barclay, Hogan, Fryers (Whitfield 62), Kitching, Collar (Walker 62), Rooney, Croasdale, Reid, Madden. Subs not used: Palmer, Rydel, Raikhy.
Shots on target: 1
Shots off target: 5
Attendance: 2,661 (868 away)
Referee: Scott Simpson
Town man of the match: Niall Maher and Tom Bradbury were superb at the heart of the Town defence, while Jordan Slew also deserves a mention, but Kieran Green gets the nod after a performance that epitomised Halifax's hard work and fighting spirit on the day.