Ward made a number of brilliant saves late in the game, and McKirdy scored one and provided another, as Ben Garner's side recorded another away victory to lift themselves to within four points of their opponents.
Story of the game
The league leaders had the first big chance of the game, as wing-back Kane Wilson cut in from the right-hand side and slid a perfectly weighted through ball into the path of Jack Aitchison.
Luckily for Swindon, goalkeeper Ward, who was making his league debut, was alert to the danger and rushed out to sweep the ball from Aitchison’s feet as he ran into the box.
The visitors replied with a chance of their own minutes later, with the ball ending in the back of Forest Green’s net as Tyreece Simpson pounced on the ball, which Luke McGee spilt as he tried to collect Harry McKirdy’s initial shot.
To the relief of the home support, the referee intervened as Simpson wheeled away in celebration, with the Swindon forward adjudged to have fouled Dominic Bernard as they tussled to pick up the loose ball.
It was a timid opening for the home side despite the early opportunity, as McKirdy tested McGee again on the half-hour mark, letting fly from just outside the box. However, the Forest Green ‘keeper was equal to it with a superb fingertip save.
That chance provided a wake-up call for Rob Edwards’ side, who looked to their frontman Jamille Matt to deliver the goods, and he almost did, rising highest from a corner only to have his header blocked on the goal line.
Nicky Cadden then forced an acrobatic save from Ward off a long-range free-kick that was sailing towards the top right corner in a tightly contested half, which lacked clear-cut opportunities for either side.
Possession was shared evenly in the half, and both teams had spells of superiority, although neither could create goalscoring opportunities for their forwards. However, this outcome was not surprising, with both teams having scored most of their goals in the second half of games to start the season.
To open the second period, Forest Green midfielder Aitchison found himself in behind the Swindon backline once again and with just the ‘keeper to beat, he flashed his shot wide from a tight angle, in what was probably his team’s best opportunity up to that point.
He was made to rue that missed chance, even more when McKirdy, the Robins’ stand-out player in the first half, got a crucial touch on Ben Gladwin’s out-swinging cross to divert the ball past McGee give the visitors the lead.
The hosts looked for a quick response to going behind and almost found one when Matt Stevens’ scuffed effort almost evaded Ward, who had to stretch low down to his right to push the ball away from goal.
McKirdy was causing issues for Forest Green throughout the game, and he came close to a second goal with just 20 minutes to play – Rob Hunt bombed forward and played a first-time cross into the path of the forward who blazed the ball over from close range.
Debutant Ward was busy for the visitors late in the game as Forest Green pushed for an equaliser, saving substitute Jake Young’s deflected effort before Stevens squandered a golden opportunity with a header from the centre of the box.
The League Two table-toppers continued to apply the pressure; however, Swindon had the unlikeliest of heroes of stand-in goalkeeper Ward who pulled off an excellent save with just ten minutes left in the game, this time denying Josh March, whose header was destined for the bottom right corner.
Swindon then rewarded their ‘keeper for his heroics with a result-clinching goal, McKirdy again the instigator as he broke free of the Rovers defence, lobbing the ball over the on-rushing McGee into the path of his strike partner Simpson who could not miss.
Ward gave away a soft penalty in the game's closing moments, which threatened to undermine his superb performance, but the Swindon 'keeper denied March from 12-yards to preserve the clean sheet.
A lack of cutting edge for Forest Green
Nothing can be taken away from the defensive performance of Swindon in the game, but in the end, Edwards will be disappointed with his side's output on the other end of the pitch.
Forest Green and Swindon set up with a 3-5-2 system which seemed to result in the teams cancelling each other out at times, with the usual suspects for Rovers were kept quiet throughout the game.
The hosts began to create more chances as the game wore on but suffered from a lack of cutting edge, uncommon for the league's top goalscorers.
The perfect away performance for the Robins
Although the hosts troubled the goal significantly in the latter stages of the game, the result never seemed in doubt for Swindon after McKirdy's goal.
They shared possession of the ball evenly with their opponents throughout the game, with the finishing touch of their forward pair Simpson and McKirdy the difference as they took all three points in the derby.
Man of the match
Swindon Town - Lewis Ward
A stand-in for Joe Wollacott, who was called up for international duty, Ward pulled off a catalogue of excellent saves, including one from the penalty spot to preserve a much-deserved clean sheet.
Making his first league appearance for Swindon, the 24-year-old made a statement to his manager to give him more opportunities going forward with a match-winning performance against the league leaders.