Two goals in the last 10 minutes secured the points after the Blades had had two goals disallowed for offside in a disjointed first half.
Top scorer Billy Sharp struck seven minutes from time with a far-post header and Jack O’Connell nodded in a second, though it was later credited as an own goal from home striker Sam Baldock.
Sheffield United had been in indifferent form, with only two wins in their previous eight matches.
Reading, after only four league victories all season, dismissed manager Paul Clement on Thursday - ending his nine months in charge. Under-23s boss Scott Marshall took over caretaker duties for the game.
The visitors made a sluggish start and allowed left-back Chris Gunter a clear sight of goal, but the Wales defender lacked composure and drilled his 20-yard effort well over the crossbar.
United at last got going with a series of promising attacks. Oliver Norwood, the Blades captain and former Reading midfielder, wasted a free-kick on the edge of the home area with a poorly directed attempt.
Conor Washington thought that he had put Sheffield United ahead from close range after John Egan’s flick-on, but he was correctly flagged offside.
David McGoldrick should then have done better after latching on to Norwood’s clever pass. However, his finish was weak as he tamely lobbed the ball into the arms of Reading goalkeeper Anssi Jaakkola.
Reading threatened mostly on the counter-attack, with Josh Sims cutting in from the right only to see his firm shot blocked.
United again had a goal disallowed for offside, this time McGoldrick the culprit as he turned in George Baldock’s near-post cross.
Reading upped the pressure as the interval approached but Sims drove wildly over after smart approach work.
Chris Wilder’s men began brightly after the break, with Jaakkola forced to make a fine save from McGoldrick’s angled drive.
They went even closer shortly afterwards when Chris Basham’s goal-bound header at the far post was nodded off the line by Gunter.
Sheffield United maintained the tempo, with McGoldrick and substitute Sharp both presented with good chances.
First McGoldrick nodded straight at Jaakkola from a Baldock cross; then Sharp found himself free in the home area only to head wastefully wide.
But Sharp made amends in the 83rd minute when he ghosted in to clip home his 12th goal of the season from a Basham cross.
Three minutes later, O’Connor appeared to make the game safe when he headed in at the far post from a John Fleck corner, though Reading striker Baldock was adjudged to have got the final touch for an own goal.