A brave second half display from the visitors proved immaterial, as ten-man Rangers succumbed to a 3-1 defeat at The Britannia Stadium.
In a first half dominated by the Potters, goals from Richard Cresswell (5) and Liam Lawrence (20) put the hosts firmly in the driving seat.
Cresswell opened the scoring with a simple far post tap-in from a Rory Delap long throw-in, before Lawrence stunned the travelling R's faithful with a set-piece special from fully 20-yards after 20 minutes.
Bad turned to worse for Rangers inside the opening two minutes of the second half, when Blackstock was shown a straight red card for a late tackle on Ryan Shawcross.
And although Rowan Vine provided brief hope when he lashed a stunning strike past Steve Simonsen from range, Stoke soon restored their two-goal buffer when Leon Cort headed home the hosts third 14 minutes from time.
Buoyed by Saturday's impressive display in the goalless draw against Sheffield Wednesday, Luigi De Canio made just a solitary change to the starting XI.
Finnish international Sampsa Timoska returned to the side at the expense of Bob Malcolm, while the fit-again Blackstock partnered Vine in attack.
Stoke boss Tony Pulis selected an attacking line-up, which included the returning Lawrence and Ricardo Fuller.
There was an early scare for the Potters, when Cresswell suffered a nose injury after an aerial tussle with Martin Rowlands.
The old cotton wool trick did the job though, stemming the steady flow of blood from the striker's nose and he soon had his say.
Rory Delap's long throw-in from the right flank evaded everyone, until Fuller hooked the ball back goalwards and the unmarked Cresswell fired home with aplomb.
The goal stung the R's into action and when Vine teed up Akos Buzsaky four minutes later, only a well-timed block denied the Hungarian international midfielder.
The respite was brief though, with a succession of Delap throw-in's asking yet more questions of a startled Rangers back-line.
The hosts were unfortunate not to be two goals to the good in the 15th minute.
Fuller cut a hole through the R's defence with ease, but - just as in the opening exchanges on Saturday - the woodwork came to the Hoops rescue, as his shot fired off the foot of Lee Camp's right hand post.
There was to be no reprieve though and moments after Michael Mancienne limped off with a hamstring injury, Lawrence lashed an unstoppable free-kick into the top right hand corner, giving Camp absolutely no chance.
Rangers looked totally shell-shocked, with the normally unflustered midfield quartet failing to assert any sort of dominance on proceedings.
Scott Sinclair provided some hope when he was freed by Vine, but as the Chelsea loanee bore down on goal, a superb covering tackle from Cort thwarted the visitors' efforts.
As the clock ticked down to the break, Rangers - with one eye on the half-time whistle perhaps - reverted to a cautious 4-5-1 formation, with Blackstock ploughing a lone furrow up-front.
Four minutes of first half stoppage time produced little action of note, although Fuller should have perhaps done better from an acute angle, blasting wide with strike partner Mamady Sidibe unmarked on the edge of the six-yard box.
Disaster struck on the resumption for the R's, when Blackstock was given his marching orders for a late challenge on Shawcross.
Referee Uriah Rennie was particularly rash in brandishing the red card, which was hardly surprising given his whistle-happy performance during a stop-start first period.
Undeterred, it was ten-man Rangers who created the first chance of the second half, when Buzsaky's right footed free-kick flew inches wide of Shawcross' right hand post.
And to their credit, it was the visitors who continued to pose the greater threat, with Sinclair seeing his shot blocked by Stephen Wright.
De Canio's bullish approach to stick with two up-front following the dismissal of Blackstock paid dividends in the 62nd minute, after a sustained period of QPR pressure.
Rowlands found Vine on the edge of the 18-yard box and the Birmingham loanee cut inside before drilling the ball past Steve Simonsen.
Buoyed by only his second goal since his loan switch from St Andrews, Vine went on the prowl for his second of the match in the 69th minute.
After robbing the otherwise exceptional Shawcross inside the Stoke half, Vine took two touches to get the ball out of his feet, before firing a low drive on target, which Danny Pugh diverted to safety.
Fuller should've put the result beyond all doubt moments later, only to inexplicably shoot over from little more than eight yards, with the goal at his mercy.
Just when it appeared as though Rangers would mount a grandstand finish, they were caught napping at the back and Cort made amends, heading home his first goal in Stoke colours to all but clinch the three points.
The sight of Buzsaky limping off in added time only served to compound the R's woes, ahead of another tough trip North to Blackpool on Saturday afternoon.
Stoke City: Simonsen, Wright (Wilkinson 82), Cort, Shawcross, Pugh, Lawrence, Delap, Eustace, Cresswell, Sidibe (Parkin 77), Fuller (Phillips 86).
Subs: Hoult, Zakuani.
Scorers: Cresswell 5, Lawrence 20, Cort 76
Bookings: Delap 90
Red Cards:
QPR: Camp, Barker, Stewart, Mancienne (Malcolm 19), Blackstock, Buzsaky, Rowlands (Bolder 82), Vine (Nygaard 78), Timoska, Leigertwood, Sinclair.
Subs: Cole, Ainsworth.
Scorers: Vine 62
Bookings:
Red Cards: Blackstock 47
Referee: Mr U Rennie
Attendance: 11, 147
