It was always going to be a tough ask to come go to Edgeley Park and get anything and so it proved, as Nyal Bell fired the Hatters in front after just ten minutes.
Captain Shane Sutton led by example to head home the Bucks' only chance of the first period on the half hour.
It was a tale of two free kicks early in the second period as match winner Matty Warburton's set piece was cancelled out nine minutes later by Brendon Daniels.
However the Bucks just couldn't keep Stockport's potent attack quiet for long, as Warburton flicked in what proved to be the winner 20 minutes from time.
It could have been all so different though, had Daniel Udoh showed more composure two minutes from time.
He was found unmarked in the box, but a heavy touch ran away from him and so did the chance to take a late point back to Shropshire.
Gavin Cowan opted for the three changes against the high flyers, and also tweaked the Bucks' system.
Marcus Dinanga was dropped to the bench, leaving Udoh to lead the line by himself, with Henry Cowans and James McQuilkin acting as two number 10s behind the front man.
Steph Morley and Darryl Knights also missed out, with wing men Brendon Daniels and Ryan Barnett recalled after sitting out the midweek draw against Guiseley.
It was safe to say the Hatters were the favourites going into this one, given their sparkling form that had seen them avoid defeat in the league since late November.
They had lost twice in 20 outings and were unbeaten in 17 games, in contrast to the Bucks who had stuttered a little of late and were without a victory in two games.
Stockport applied the early pressure as Darren Stephenson had a shot blocked, and the Bucks defence had to withstand a couple of set pieces.
The games first talking point came up the other end though after seven minutes, with the visiting fans and players calling for referee Mike Barlow to produce a red card.
From a County corner Telford broke and McQuilkin looked to have set Udoh clear, but the sharp shooter was upended by Scott Duxbury who appeared to be the last man.
But despite big shouts from the Bucks players for the official to produce a red card, the defender escaped with just a caution.
Then with their next attack the potent Stockport strike force stuck, with a little help from the visitors.
With the Hatters advancing forward, Ross White slipped on the edge of his own box, allowing Bell to drive into the area and calmly slot the ball past Josef Bursik.
County were looking dangerous in the final third, as you would expect from a side on the coat tails of the league leaders.
Sam Walker saw a goal bound effort deflected wide as the hosts went in search of an early two goal buffer.
It bizarrely got a bit tasty between the two dugouts on the quarter hour mark, as Bursik went down for treatment and Cowan called his troops in for a team talk.
It seemed the Stockport bench were unhappy with this, with a few words exchanged between the two sets of back room staff.
On the field Bell sprung the offside trap soon after but was beaten to the ball by Bursik, before Stephenson could only direct a shot wide of the near post from a low cross.
The Hatters were looking comfortable and the more likely to score, with Telford showing little in the way of a threat going forward.
Udoh was isolated without a striker partner, and the Bucks didn't seem as fluent in the attacking third as they usually do.
It didn't matter though as they worked a set piece to perfection just after the half hour mark to draw level.
Daniels fired in a corner and captain Sutton timed his run to meet it, and power a header down into the corner of the net giving Ben Hinchliffe no chance in the Hatters goal.
On the face of the scoreline it was so far so good for the Bucks, but they hadn't been as fluent or threatening in the first half as boss Cowan would have liked.
That proved to be the case and the Telford chief changed things at the break.
Amari Morgan-Smith was thrown on from the bench to offer more support to Udoh up front, with Cowans the man to be sacrificed.
Within six minutes of the re-start though the visitors found themselves behind for a second time in the game.
They conceded a free kick on the edge of their own box, and Warburton stepped up and curled the ball into the far corner beyond Bursik.
The on loan Stoke stopper got something on it, but not enough to prevent it from creeping into the corner.
Anything Stockport can do though, Telford can do too and so it proved less than ten minutes later
Morgan-Smith was upended on the edge of the Stockport area, and free kick specialist Daniels fired under the wall and past Hinchliffe to level it up.
Telford just couldn't hold the lead though as County went back on the offensive, and got in front for a third time just seven minutes later.
Jordan Keane crossed from the right side, and Warburton drifted in to turn in his second of the afternoon.
It could have been all over in the next attack, but the Bucks had White to thank for keeping them in it.
McQuilkin conceded possession in his own half and the dangerous Stephenson beat his man, and fired past Bursik.
However White was at the back post to scramble it clear.
Stockport wanted that fourth to kill of any chance of a third comeback from the visitors.
Duxberry was denied by a brilliant Sutton tackle in the six yard box, with Adam Thomas dragged a shot narrowly wide of the Bucks upright.
Telford needed a late spark and boss Cowan was hoping it would be Dinanga, as the former Burton man was thrown on with the visitors going with three up for the last five minutes.
They hadn't really had any chances from open play throughout the game, but in the 92nd minute the front three combined and the Bucks really should have snatched a point.
Dinanga's ball over the top found Morgan-Smith, and he squared for an unmarked Udoh in the box.
But the usually clinically striker's touch was too heavy, with the ball running away and the goalkeeper smothering his effort.
7 - POSSIBLE RED CARD? - Telford break from a County corner, with James McQuilkin finding Daniel Udoh who beats Scott Duxbury, before the defender pulls him down. Udoh looked to be in on goal, meaning Duxburry is technically the last man. Despite big claims for a red, referee James Gannon only produces a yellow card.
10 GOAL - Stockport apply the early pressure and it tells just ten minutes in. Ross White slipped under pressure on the right in the final third, and Nyal Bell took advantage. He pinched the ball before driving at goal and slotting the ball into the far corner, beyond Bursik.
15 - CHANCE - The home side go close to a second. A corner is punched by Bursik, it is recycled and comes back into the box. The ball falls nicely for Sam Walker, who meets the it on the edge of the area, but his goal bound effort is deflected just wide.
33 - EQUALISER - With their first chance of the game, the Bucks claw themselves level. Set piece specialist Brendon Daniels fires in a flat corner that is met perfectly by captain Shane Sutton, who heads it down and into the corner.
51 l GOAL l Telford concede a free kick in a dangerous position and the Hatters get their noses back in front. Warburton steps up from the edge of the box, curling a low effort around the wall and in. Bursik got a hand to it, and arguably should have done better.
62 - LEVEL AGAIN - Anything you can do we can do to say the Bucks. Amari Morgan-Smith is upended and Brendon Daniels steps up to curl a free kick under the wall and in.
69 - GOAL - The lead lasts all of seven minutes. Jordan Keane crosses from the right and Warburton drifts in to turn home his second of the game.
90+2 l GOLDEN CHANCE l The front three combine and the Bucks should have grabbed a point. Dinanga to Morgan-Smith, who squares it for Udoh in the box but his touch is too heavy and the chance goes.
Stockport County (4-2-3-1) - Hinchliffe, Minihan, Duxbury (Turnbull 55), Keane, Palmer, Baines, Thomas, Walker, Bell (Mulhern 46), Warburton (Osborne 84), Stephenson
Subs not used - Ormson, Kirby
AFC Telford United (3-4-2-1) - Bursik, White, Sutton, Streete, Royle, Deeney, Barnett, Daniels, McQuilkin (Dinanga 82), Cowans (Morgan-Smith 46), Udoh
Subs not used - Morley, Knights, Brown
Referee - Mike Barlow
Attendance - 4,708