The victory for Neil Warnock's runaway leaders on Monday evening means they are now just three wins from guaranteeing promotion and, crucially, put them 13 points ahead of Cardiff in third.
If results elsewhere go their way Rangers could even be celebrating promotion at Barnsley in eight days, with five games to spare, such has been their dominance this term.
By contrast, Sheffield United are staring at life in League One just four years after relegation from the top flight under Neil Warnock.
Micky Adams is their fourth manager of the season - the sort of turnover common at Rangers not so long ago - but they have won just twice since he took charge 17 games ago and are seven points adrift of safety.
Rangers did not have it all their own way - Daniel Bogdanovic had a shot cleared off the line and Stephen Quinn wasted another good chance - but the Loftus Road faithful are already looking forward to rubbing shoulders with west London neighbours Chelsea for the first time in 15 years next season.
They could have taken an early lead when Adel Taarabt, back in the side having missed their last match after hearing the news his cousin had been shot dead, crossed for left-back Clint Hill, who would have scored had he got more than the faintest of touches at the near post.
The hosts looked capable of scoring every time they went forward, though, and they made the breakthrough just before the half-hour.
Faurlin's chip found Heidar Helguson and his cross from the byline was swept in first time by Routledge from eight yards out.
Rangers were inches away from a second when the unlikely figure of right-back Bradley Orr strode forward and curled narrowly wide.
But United had their chances to hit back before the break, only for Shaun Derry to hack Bogdanovic's effort off the goal-line and Quinn to scuff a close-range shot wide.
However, they were down and out six minutes into the second half when Taarabt's corner was cleared by Matthew Lowton to Faurlin, who smashed it straight back into the net from the edge of the box.
Routledge added a third in the 66th minute, rounding off a neat move between Tommy Smith and Helguson to fire across Steve Simonsen.
It could have been worse for the visitors with Patrick Agyemang blazing over and Simonsen saving from Smith, but the Rangers bandwagon shows no sign of slowing down while the Blades are surely going down.