The Londoners had failed to beat United in their last eight encounters in all competitions, but had an irrefutable advantage within the opening 23 minutes courtesy of three quick-fire goals.
The impressive Hogan Ephraim broke the deadlock in the 11th minute after smartly finishing a one-on-one, before then turning provider for Jamie Mackie to head home.
The result was out of doubt in the 23rd minute when keeper Steve Simonsen hauled down Adel Taarabt, who then stepped up to score the resulting penalty.
While United boss Kevin Blackwell's programme notes had promised a "spirit of renewed hope and anticipation" his side collapsed as QPR started a league campaign with back-to-back wins for the first time in nine years.
Heading into the match, Blackwell made four changes to the starting XI that were embarrassed by npower League One outfit Hartlepool in midweek, while Warnock started fellow former United pair Shaun Derry and Paddy Kenny.
The latter was making his first return to Bramall Lane since ending his eight-year spell at the club and was welcomed by a barrage of abuse.
The chorus only grew louder as the 32-year-old trotted towards the Kop but soon the home support had other gripes to shout about.
United felt striker Jamie Ward had been hauled down in the penalty area but referee Andy Woolmer waved away the protests, allowing QPR to break forward and, ultimately, the deadlock.
The visitors' rapid counter-attack put Ephraim free down the left and he duly jogged forward before slotting under keeper Simonsen in the 11th minute.
QPR continued to threaten down the flanks and soon doubled their advantage when Ephraim delivered a superb left-wing cross for Mackie to stoop in and header home at the back post.
Rangers continued to exploit the space gifted to them down United's visibly vulnerable right side and soon increased the deficit to three goals.
Again Ephraim was allowed to waltz forward and although Simonsen managed to parry his shot, the keeper's attempts to grab the ball saw him trip the incoming Taarabt, with the Moroccan scoring the resulting penalty.
The third goal resulted in calls for the heads of both Blackwell and referee Woolmer, with the latter continuing to frustrate Blades fans by turning down an obvious penalty as the half came to a close.
The home support's rendition of their Greasy Chip Butty anthem was notably quieter after the break, although renditions of "Blackwell out" became more raucous throughout the second half.
The Blades did up the tempo and occasionally managed to challenge the Rangers back-line, although Kenny was more than a match for their sporadic efforts as QPR rode to a resounding away victory.