Barry Corr set the Robins on their way with a goal inside the first five minutes before Mansfield defender Jon Olav Hjelde headed into his own net killing the contest off before half-time.
The win maintained Swindon's six-point lead over fourth place MK Dons and they can secure promotion to League One at the West Country Derby against Bristol Rovers next weekend.
Swindon's biggest crowd of the season witnessed a dream start when Corr prodded them into an early lead from Lee Peacock's cross.
Strike partner Blair Sturrock had struck the inside of the post moments earlier before Peacock reacted quickest to set up the on-loan Sheffield Wednesday striker.
The signs were all there that the 10,472 strong crowd were going to witness a rout when Corr hit the woodwork twice in the space of as many minutes.
First, Mansfield keeper Jason White tipped his header on to the far post. And from the resulting corner the Irishman then found himself in space at the far post but frustratingly drove his effort against the frame of the goal.
Despite the whirlwind start Swindon failed to capitalise on Mansfield's paper-thin squad with manager Billy Dearden forced to pick a handful of teenagers who have never played for the first team before.
It took Hjelde's own goal to settle the nerves though as the Norwegian finished spectacularly past his own keeper from a Sofiane Zaaboub corner.
Mansfield almost clawed back a goal on the stroke of half-time when a hoisted free-kick found Barry Conlon in space. The big striker directed his header over Phil Smith but the Swindon keeper arched his back and leaped to tip over the crossbar.
With news emerging that MK Dons had gone into a 2-0 lead at Stockport, Swindon appeared to take their foot off the gas slightly and took pity on Mansfield.
Strikers Sturrock and Peacock missed golden opportunities towards the end as the promotion race goes to the wire.