Chris Morgan marked his first game in temporary charge of the Blades with a home win.
The strike-pairing he named both scored - Chris Porter and Dave Kitson both directing home Tony McMahon crosses.
In a rip-roaring first half the fired up Blades created no less than 12 chances and Swindon were forced to kick off their own line on three separate occasions.
Chris Morgan's first team selection saw McMahon and Porter recalled with Higginbotham and Forte dropping to the bench, where they were joined by Whitehouse, who was also added to the list of substitutes.
Tracksuited and flanked by David Unsworth, Morgan received a rapturous reception from the Unitedites, who saw their favourites quickly on the offensive. Within a minute a cross by Murphy was turned over the crossbar by McDonald and moments later a McMahon inswinging free-kick appeared to touch Maguire on the way to connecting with a post.
For Swindon, Luongo's half-volley was straight at Long but the visitors were struggling to cope with United's electric start and between minutes 9 and 13... there were FIVE good chances.
Firstly, both Porter and Kitson were denied by goal-line clearances in the same move and then Murphy's shot, after cutting inside, was saved by the goalkeeper after intelligent passes from Doyle and Hill. Porter was also denied by Foderingham after racing onto a Kitson pass and the overworked goalkeeper also kept out a long-ranger from Murphy.
Following a foul on Porter, a quick free-kick by Kitson caught on Swindon but Doyle was unable to capitalise and poked wide on 20 minutes, then Porter was put through again by Kitson but the subsequent shot was across goal and wide. The highly involved Porter then charged down a clearance by Foderingham but luck was on the goalkeeper's side and he recovered.
Long was twice called into action, pushing over a De Vita shot and rushing off his line to prevent Williams connecting with a short back-pass from Collins... but between those efforts the Blades had deservedly taken the lead.
Swindon, who picked up four first half bookings, were conceding free-kicks in dangerous positions and from one, on 37 minutes, McMahon's delivery from the right was met by PORTER, who held off his marker and headed home from close range.
There were two further, good chances for the Blades to extend the lead. Flynn raced on to a Collins pass as Swindon switched off but his effort, after holding off the attentions of Flint, was kicked off the line by McCormack, who then conceded yet another free-kick which McMahon curled against a post with Foderingham scrambling.
Swindon must have wondered what had hit them when they trudged off at half-time, whilst Blades fans were off their feet and applauding as the players disappeared for a deserved cuppa.
The visitors made the better start to the second half, applying a little pressure, but all they had to show for the first 15 minutes of the half were shots from Byrne and substitute Rooney, both of which were off target. Ward also headed wide a corner from Ferry soon after.
For United, McMahon blazed a free-kick over, whilst Morgan's first change was replacing Murphy with McFadzean. Blades fans got excited on 73 minutes when Ferry deflected Doyle's cross into the path of Kitson but the Swindon midfielder recovered to prevent the striker getting a shot away.
Whitehouse was handed a home debut when he replaced McDonald with little over ten minutes to play - and soon after the Blades were celebrating again.
KITSON, who played an important role in winning the throw from which United scored, got a deft touch to McMahon's curling cross and although Foderingham got his hand to the ball, he was unable to keep the ball out of the Kop net.
Porter received an ovation when he was replaced by Ironside moments later and the young striker had a shot blocked before Long was called upon to palm away a shot from Francis.
On 88 minutes McFadzean latched on to Doyle pass but shot just wide when moving at pace, whilst five minutes of added time were comfortably negotiated, despite Luke Rooney shooting wide and Whitehouse slicing an attempted clearance across goal!
Blades: Long, Maguire, Hill, Flynn, Doyle, Porter (Ironside 84), McDonald (Whitehouse 79), Kitson, N. Collins, Murphy (McFadzean 70), McMahon.
Unused: Higginbotham, Forte, Robson, Coyne.
Swindon: Foderingham, Flint, Ferry, J. Collins (Francis 72), Roberts (L. Rooney 62), McCormack, Williams, Ward, De Vita (A. Rooney 56), Byrne, Luongo.
Unused: Devera, Navaro, Bedwell, Waldon.