The Stags struck after just two minutes with their first goal from open play in 548 minutes and never looked back, recording their first win in five games to wipe away the misery of conceding an injury-time equaliser in the FA Cup just three days earlier.
Swindon rarely looked likely to launch a comeback, their best chance falling to Lucas Jutkiewicz who fired across the face of goal five minutes from time.
The in-form Robins lost former Stags star Lee Peacock to injury before the kick-off. And after just three minutes they were left needing his firepower as the Stags took a shock lead with their first goal from open play in six outings.
Jon Olav Hjelde flicked on a Matt Hamshaw cross and Richie Barker stabbed in his 13th goal of the season from close range.
A minute later Hjelde was in the action at the other end, deflecting Ady Williams' 20-yard drive over keeper Carl Muggleton and onto the bar.
The Stags, despite playing in front of their lowest home league attendance of the season, continued to raise their game against the high-flying Robins.
And Simon Brown almost doubled their lead in the 14th minute, flicking Barker's chipped cross narrowly wide after a fine break away led by Michael Boulding.
Six minutes later Brown squandered an even better chance, firing straight at Phil Smith from six yards after a kind ricochet in the area.
Mansfield were almost made to pay for wasting those chances when Ricky Shakes blasted wide, Williams headed just over from a Jack Smith free-kick and Jutkiewicz nodded a Shakes cross straight at the keeper.
But the home side, coping better with the blustery conditions, continued to create the better chances. A quick throw from Jake Buxton put Barker clear in the area and his first-time shot zipped into the side-netting.
Brown wasted yet another opportunity in the 38th minute, sliding in at the far post to knock an excellent Barker flick-on wide from point-blank range.
But within 30 seconds it was fourth time lucky as he was celebrating a goal at last, racing clear onto Hamshaw's fine pass to round the keeper and score only his second goal of the season - his first since a long injury lay-off.
Swindon inevitably came out fired up for the second half and forced two quick corners, but it was the home side who went closest to a further goal in the 51st minute when Hamshaw broke clear before watching Smith save his low, drilled low shot.
The keeper did well to hold on to another long-range effort, this time from Giles Coke, as the home side continued to dominate with their tough tackling, quick passing and strong running.
Swindon finally carved out a chance of their own through Jutkiewicz, whose curling 61st minute drive was pushed away by the diving Muggleton.
Disappointing leading scorer Christian Roberts was replaced after just 61 minutes as Robins manager Paul Sturrock desperately tried to inspire a fight-back that never materialised.