The visitors struck the woodwork in the first half and had two penalty appeals turned down but couldn't break down the Blades.
Mark Cooper made just one change to his starting XI with striker Jon Obika returning to the partner Andy Williams up front while Michael Smith dropped to the bench. There was also a place among the substitutes for Lee Marshall.
In a fiery first half at Bramall Lane, Swindon had the best of the opening exchanges. Harry Toffolo arrowed a free-kick narrowly wide before John Swift planted an effort straight at Blades’ ‘keeper, Ian Turner. The stopper would also deny Jack Stephens from distance later in half.
Che Adams, the home side’s hero against Tottenham earlier in the week, created United’s first chance of note when he brought down a raking, cross-field ball before curling a shot which just evaded the dive of Wes Foderingham and the far post.
Meanwhile, Town spurned another chance to go in front at the other end. A spell of pinball in the box ended with Swift lashing an effort off the crossbar and over.
Before the half was over, the home side were handed another opportunity to take the lead. A free-kick on the edge of the Town box ended with the ball striking Foderingham’s right-hand upright and rolling across the face of goal before being cleared.
At the start of the second period, the visitors created a chance for Andy Williams but the frontman could not get enough power on his shot to test the goalkeeper.
The home side made the breakthrough midway through the second half. After working some space on the right, the ball in was met by Jamie Murphy who swept the it home past Foderingham.
Louis Thompson drilled a shot narrowly wide as Swindon looked for a way back into the game while Harry Toffolo went down under a challenge in the box but the referee waved away appeals for a penalty.
Deep into stoppage time, with Town committing bodies forward in search of an equaliser, the hosts sealed the game with a breakaway goal. Murphy again was the beneficiary, striding forward on his own from the halfway line before lifting the ball over the advancing Foderingham and into the net.
Town had a second spot kick appeal turned down in stoppage time as Jordan Turnbull appeared to be fouled in the box but, once again, the visitors' protests fell on deaf ears.