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A Billy Paynter penalty was enough to claim all three points for Town on a bitterly cold evening at Edgeley Park.
Struggling Stockport made a bright start to the match, with new loan signings Jabo Abehre and Jemal Johnson making a foray or two into the Town box.
As expected, the game was a far from attractive affair in the early exchanges, although to their credit, both sides attempted to play a passing game on an uneven surface.
Colchester United loanee David Perkins was particularly impressive for the hosts as he orchestrated their first sustained period of pressure, which saw both Ibehre and Danny Pilkington test David Lucas from range.
Town began to keep possession a little more after the home side's early pressure, but still found it hard to string a series of passes together as the ball would seldom run true.
The visitors looked increasingly comfortable in the following period, and Charlie Austin thought he had bagged his 9th goal in as many games, but the linesman's raised flag quickly curtailed his celebrations.
With the half moving into its final ten minutes there was only one side in it, with Gary Ablett's side camped in their own half, and requiring last ditch blocks to deny both McGovern and Ferry.
After two decent spells of pressure from both sides, the half drew to a scrappier close with chances at a premium, and the teams went in level at the break.
As they had done in the first, the home side started the better of the two sides in the second half, and could have gone ahead had it not been for an excellent save from the back pedalling David Lucas. Jemal Johnson nodded home the rebound but was comfortably offside.
Stockport continued to exert pressure on the Town goal, and could have gone in front with a cross shot from Danny Pilkington which flashed across the six-yard box and narrowly out of the reach of Jemal Johnson.
Mid-way through the second half the pitch began to cut up and hindered the quality of the match even more than it had in the first.
However it was one piece of quality that broke the deadlock. An impressive cross-field ball from Gordon Greer pick out JP McGovern, who touched the ball neatly inside and allowed Kevin Amankwaah to break into the box.
Amankwaah broke across County's Michael Rose, and an outstretched hand from the left back grabbed Amankwaah's shirt, who went down under the challenge and the referee pointed to the spot.
Billy Paynter stepped up to hammer the ball into the roof of the net to register his 14th of the season and put Town 1-0 up.
It was then the visitors who began to dictate the pace of the game as a deflated looking Stockport struggled to regain any of their early momentum.
Ibehre and Rose tried their best to level the scores with efforts from long range, but it was testament to Town's late dominance that these were the only chances County could muster.
The home side will feel aggrieved to have lost a game in which they played very well for long periods. However, Town put together the best move of the match, and were rewarded with a penalty and the points from a turgid evening's football at Edgeley Park.
STOCKPORT COUNTY 0
SWINDON TOWN 1 (Paynter '78 pen)
Stockport County: Owain Fon Williams; Johnny Mullins, Danny Swailes, Michael Raynes (Capt.), Michael Rose; James Vincent, David Perkins, Richie Partridge, Danny Pilkington (Greg Tansey '84); Jabo Ibehre, Jemal Johnson
Substitutes: Paul Gerrard (GK), Paul Turnbull, Greg Tansey, Andy Halls, Declan Edwards, Danny Rowe, Sam Barnes
Bookings: Pilkington '77
Swindon Town: David Lucas; Kevin Amankwaah, Gordon Greer (Capt.), Scott Cuthbert, Lecsinel Jean-Francois; Danny Ward, Simon Ferry, Jonathan Douglas, Jon-Paul McGovern; Charlie Austin, Billy Paynter
Substitutes: Phil Smith (GK), Sean Morrison, Craig Easton, Michael Timlin, Lloyd Macklin, Ben Hutchinson, Mark Marshall
Referee: Mr G Salisbury
Attendance: 3281 (213 away)
7.15pm - The teams are in. Lecsinel Jean-Francois replaces the injured Alan Sheehan at left back, while Vincent Pericard (tight hamstring) did not travel as a precaution. The home side include all five of their recet loan signings.
7.35pm - The players return to the changing rooms ahead of kick-off in one of Town's crucial games in hand. There is no doubt about it, it is painfully cold. At least there is an entertaining 90 minutes of football ahead.
7.45pm - The match kicks-off at a sparsely populated Edgeley Park.
7.50pm - First half chance of the game for Town, as Charlie&nbsp;Austin steals across the front post but pokes JP McGovern's cross wide.
7.53pm - Town appeals for a penalty are turned down as Kevin Amankwaah goes to ground on the edge of the Stockport box.
7.54pm - David Lucas is called into action for the first time, as David Perkins cuts inside Amankwaah and lays the ball off to Danny Pilkington whose long range shot is hel well by the former Leeds United stopper.
7.55pm - James Vincent beats Lecsinel Jean-Francois on the right, and his cross breaks loose in the box, but Gordon Greer flys into a challenge with Jabo Ibehre and clears the danger. A decent spell of Stockport pressure comes to an end.
7.58pm - Ibehre makes space for himself on the edge of the box, and gets a powerful shot away which is saved sharply by Lucas at his near post.
8.03pm - Excellent work from Richie Partridge on the right, as he beats Jean-Francois and squares the ball to Jemal Johnson, who shoots from the edge of the box and forces Lucas into a sharp save to his left.
8.10pm - Billy Paynter finds space on the right wing and crosses deep towards Austin, but the in-form striker can't quiet reach the ball as it bounces out for a goal kick.
8.12pm - Austin has the ball in the back of the net but turns around to see the linesman's flag aloft. Danny Ward's right footed shot had been blocked and broke to Austin inside the box, who rolled the ball home after his initial shot was blocked, but the goal was ruled out.
8.16pm - Jean-Francois crosses well towards Paynter who heads across goal towards McGovern, whose powerful shot it blocked well by Danny Swailes and loops out for a corner, which is dealt with by the increasingly under-pressure home side.
8.19pm - Simon Ferry does well to hold off a challenge on the edge of the box and lays the ball off to Austin, who curls a speculative shot over the bar from 25 yards out.
HALF TIME Stockport County 0 Swindon Town 0
8.45pm - The second half kicks off.
8.50pm - It's County's turn to have a goal disallowed as a looping from Ibehre sees Lucas back track and make a wonderful save. The ball loops onto the edge of the six-yard box and Jemal Johnson nods home, but as he was offside from the original cross, Johnson's goal is chalked off.
8.58pm - JP McGovern sets the over-lapping Kevin Amankwaah away down the right flank, and the right back's cross reaches Paynter at the back post, who takes a touch and blasts wide of the near post when he might have done better.
9.05pm - A neat turn from Austin on the edge of the box sees him set Paynter free inside the box, but the big Scouser's shot is straight at Fon Williams in the home goal.
9.06pm - At the other end, a poor clearance lands at the feet of Danny Pilkington, who's shot flashes across the face of goal and is narrowly missed by Johnson at the back post.
9.13pm - PENALTY! A glorious long range pass from Gordon Greer picks out McGovern who plays in Amankwaah, and Michael Rose pulls him over. Up steps Paynter....
9.14pm - GOAL! Paynter rifles the ball into the roof of the net to put Town 1-0 up.
9.23pm - Town beginning to exert some dominance over proceedings for the first time in the match.
9.23pm - SUBSTITUTION: Greg Tansey on to replace Danny Pilkington.
9.25pm - Jabo Ibehre does well to hold off the challenge off Cuthbert, but flashes his shot way over the bar.
9.29pm - Paynter flicks on towards Austin, who has a speculative attempt from 30 yards which flys narrowly over.
FULL TIME Stockport County 0 Swindon Town 1