Iliman Ndiaye was the hero for the Blades on the night before limping off later with an injury, giving United something of an injury concern ahead of more key games coming up.
But United showed their character to bounce back from Saturday's disappointing defeat at Blackburn, with would-be new owner Dozy Mmobuosi watching on from the stands.
Here's how we rated United’s players in victory in Berkshire...
1. And he wears the 29...
Sheffield United's Iliman Ndiaye (centre) gets away from Reading's Tom Holmes (on ground): Nick Potts/PA Wire. Photo: Nick Potts
2. Wes Foderingham 7.5
Untroubled in the first half apart from a late coming-together with Tom Ince after the Reading man stuck a leg out and fouled the United goalkeeper, which saw him booked. Made a superb stop later in the game to tip over Carroll's dangerous header Photo: Paul Terry
3. Jayden Bogle 6.5
A brilliant driven ball across the face of goal was begging to be converted but went begging - before another attempted centre was ballooned into the stand. Attracted the frustration of John Egan in particular after overplaying and losing the ball on the wing, leading to a Reading counter-attack, Great ball in behind led to United's opener Photo: Warren Little
4. Chris Basham 7
Showed typical Basham bravery and courage to throw his head where the boots were flying and protect the lead, taking a whack for his troubles and leaving his teammates incensed that the game was not immediately stopped with Basham stricken on the turf. Photo: Warren Little