Goals in the 70th minute for Neill Collins and Billy Sharp in the 75th minute were enough to seal all three points for the Blades who ended Swindon’s four-match unbeaten League record.
Brandon Ormonde-Ottewill and Nathan Thompson missed out for Town through illness and injury and were replaced by Kevin Stewart and Drissa Traore.
Sheffield United kicked off playing towards the Town End and earned a corner in the 1st minute thanks to a defensive clearance although Lawrence Vigoroux caught the resulting cross cleanly.
Town’s first attack in the 6th minute saw Fabien Robert play a good one two with Drissa Traore before sending a dipping shot just over the bar with the United keeper Mark Howard backpedalling.
There was a break in play when Kevin Stewart took a knock but he was able to continue after treatment.
Nathan Byrne tried his luck from the edge of the area in the 8th minute after picking up a loose ball when Turnbull had chased down what looked like a lost cause and Byrne also fired in another shot just wide shortly afterwards from a similar position.
Michael Williams did well to deny Campbell-Ryce who was bearing down on goal with the Town defender flicking the ball out for a corner which led to a free kick for Town when Vigoroux was fouled.
Midway through the half Lawrence Vigoroux did well to push a goalbound shot by Louis Reed out for a corner and the Blades almost went ahead when the ball was crossed through Sammon but his close range shot struck the crossbar and the ball rebounded to safety.
The game was proving to be a close affair with Town not getting as much possession as in recent games with much of the play centred in midfield as the half wore on.
Drissa Traore drew good applause from Town fans after he denied Sammon then Campbell-Ryce from launching attacks down the right wing before setting up a Town attack.
Connor Sammon went close for the Blades in the 31st minute with a flicked effort from a cross but his effort went narrowly over the crossbar with Vigoroux beaten.
Rossi-Branco drew a foul in the 34th minute which led to a free kick and the Brazilian then popped up in attack when the ball was crossed but his header went wide of the upright.
Jordan Williams was cautioned in the 38th minute for a late challenge on the halfway line which broke up a dangerous looking attack.
Town started increasing the pressure on the visitors with some good moves which led to Kasim firing just wide as the match entered the 45th minute.
One minute of added time was played before the half time whistle was blown by the referee Chris Sarginson to end the goalless first half.
Town kicked off and enjoyed some good possession but were penalised in the 50th minute for handball by Traore which led to a corner when Branco headed behind from the freekick.
A flowing Town move saw Robert head just wide after Kasim had started a good move in midfield in the 51st minute.
Town were penalised in the 53rd minute for a late challenge just outside the penalty area but the initial kick struck the defensive wall before an offside flag eventually ended the attack.
Lawrence Vigoroux gave the Town fans a scare when he tried to outsmart the Blades attack with some fancy footwork on the edge of his area but eventually he managed to knock the ball clear downfield in the 57th minute.
United manager Nigel Adkins replaced Che Adams with Martin Woolford in the 61st minute.
Fabien Robert’s persistence almost led to an opener for the Robins when he managed to gain possession on the edge of the visitors penalty area before firing just wide of goal in the 63rd minute.
Town continued to enjoy plenty of possession with Sheffield happy to pack their defence and soak up pressure and catch Mark Cooper’s side on the break.
Michael Smith left the field to good applause in the 67th minute when he was replaced by Miles Storey.
The visitors were awarded a corner in the 69th minute but the Town keeper Vigoroux took the resulting cross cleanly.
Disaster struck in the 70th minute when the Town defence failed to clear from a corner conceded by Stewart and the ball ended up in the home net after Reed had bundled the ball forward for Neill Collins to head home.
The visitors doubled their lead in the 75th minute after exploiting a massive gap in Town’s midfield and the ball fell to Billy Sharp who sidestepped Williams’s challenge to sidefoot the ball past Vigoroux to the delight of the 1117 visiting supporters in the crowd of 8614.
Town’s day got worse in the 78th minute when Vigoroux saw yellow for a late challenge on Sharp about 30 yards from goal after he had outpaced the defence but the referee decided that the keeper had not denied an obvious goalscoring opportunity so a caution was the outcome and the Town keeper took up his place to defend the freekick.
Rossi-Branco saw yellow for a late challenge as Town’s discipline slipped but they eventually regained their composure.
The visitors replaced Campbell-Ryce with Craig Alcock in the 88th minute and also replaced Conor Sammon with Michael Higdon in the 90th minute.
Four minutes of added time were played but Town were unable to trouble the visiting keeper before the final whistle was blown to end a match where Town had been punished for failing to make the most of their chances while the visitors were more clinical in attack.