United moved into the top two of the Sky Bet Championship, with another home maximum.
David McGoldrick's tenth of the season proved to be enough to see of Steve McClaren's Queens Park Rangers, with United keeping a third straight clean sheet.
For the clash against the R's, Basham returned after suspension, taking the place of Cranie, with new recruits Dowell and Madine amongst the substitutes.
Inside four minutes the Blades should have been ahead. Baldock's diagonal ball found the run of Sharp and the skipper unselfishly laid it off to McGoldrick, but he side-footed his effort wide from a very promising position. United continued to force the issue, with Cousins booked for a late challenge on Fleck.
The game was pretty even, but United registered another attempt on target as Norwood tested Lumley. And in the 37th minute, it was the home side who deservedly put themselves in the lead. Some patient build-up play on the right ended with Norwood whipping in a cross to the near post and MCGOLDRICK got across his marker to header home past Lumley.
The first action of the second-half saw Fleck booked for a foul on Eze which stopped a potential counter-attack. With 22 remaining, Dowell received a warm applause, as he took the place of Duffy. There had been little action of note, with both sides struggling to create any goalscoring opportunities.
QPR looked to break, but Freeman's shot was tame and easy work for Henderson. Dowell was then cautioned for stopping a break. The Blades were denied twice from consecutive corners, with Basham and then Egan seeing headers deflected clear.
Seven minutes remained, as Clarke took the place of Sharp. Stevens found himself in a decent position on the edge of the box, but dragged an effort inches wide. At the other end, Freeman picked the ball up and fired a shot at goal, but thankfully it went wide.
Three minutes of added time were signalled and Stearman was introduced, taking the place of McGoldrick. Wells got to a loose ball first, before Stearman, but fired high and wide as the Blades saw the game out for a fourth consecutive league success.
Blades: Henderson, Baldock, Stevens, Fleck, O'Connell, Basham, Sharp (Clarke 83), Egan, Norwood, McGoldrick (Stearman 90), Duffy (Dowell 68).
Unused: Madine, Coutts, Johnson, Moore.
QPR: Lumley, Furlong, Bidwell, Freeman, Cousins (Smith 73), Eze, Scowen (Chair 83), Wszolek (Osayi-Samuel 62), Wells, Lynch, Leistner.
Unused: Ingram, Hall, Manning, Oteh.