Jake Young opened the scoring for the Robins with a stunning long-range effort but Harrogate made it 1-1 in the second-half through Jack Muldoon.
Over 3,000 fans were reported to be in attendance for the full-blooded affair, which proved almost as tiring as it was entertaining.
The first-half was played a high tempo, with both sides showing little attacking restraint.
Harrogate were particularly threatening on the break, launching a string of swift counter-attacks that caught Swindon cold.
Abraham Odoh was the first to benefit from Harrogate’s pace in transition, but saw his left-footed strike palmed away by Murphy Mahoney.
As quick as Harrogate were to turn defence into attack, they also looked vulnerable when Swindon probed.
The hosts were caught flat-footed in defence as Dan Kemp raced in behind, and were fortunate to see the Swindon midfielder squander the chance with two heavy touches.
Swindon were then caught out in similar fashion, as Sam Folarin darted in behind before their high defensive line. Mahoney, however, stood his ground well to thwart the forward.
It was a moment of individual brilliance that eventually opened the scoring, with Swindon marksman Young providing the magic.
The forward, on loan at the County Ground from Bradford City, pushed the ball on to his right foot before bending into the top corner from distance.
Undeterred by Swindon’s opener, Harrogate immediately went searching for an equaliser. A game of pinball ensued in Swindon’s box but Odoh and Muldoon sliced their shots.
Mahoney was then called into action once again by Folarin, who had the goalkeeper scrambling to keep out his low drive.
The relentless pace of the encounter continued into the second-half, with both sides going for the jugular.
Charlie Austin latched on to a Swindon corner but saw his flicked effort pushed round the post by Jonathan Mitchell.
A golden opportunity then fell to Odoh, who was released by a beautifully weighted defence-splitting pass from Anthony O’Connor. His shot was well-struck but fired narrowly wide of the post.
Minutes after his miss, Odoh was involved in a slick move that resulted in Harrogate’s equaliser. He combined well with Folarin and helped work the ball to Muldoon on the edge of the box.
After steadying himself, the forward unleased a powerful strike that clipped the post on its way in.
A win was evidently the target for both sides, as they committed bodies forward in search of the elusive winner.
Williams Kokolo expertly rolled away from his marker in the box before being denied by Mitchell at point blank range.
At the other end, a quick throw-in from Odoh put Folarin through on goal but hesitation before shooting ensured Mahoney came out on top.
Despite the best efforts of the attackers on the pitch, both defences held firm and the spoils were shared in North Yorkshire.