Jonathan Walters' hat-trick secured the win for Mark Hughes' side as the visitors capitulated to an 11th consecutive top-flight defeat away from home this term.
Mistakes from Karl Henry and Eduardo Vargas gifted Stoke goals in the opening 45 minutes, with Walters converting twice before Niko Kranjcar pulled a goal back.
An injury to captain Ryan Shawcross blighted the first half for the hosts and they struggled to find their momentum after the break.
QPR failed to take advantage, though, with Asmir Begovic only called into action once, the goalkeeper saving well from Vargas' acrobatic volley just before the hour.
Joey Barton was denied a late leveller when his free-kick rattled the crossbar, but the day belonged to Walters as he netted a third to move Stoke into ninth place in the table, while QPR missed the chance to climb out of the bottom three.
Stoke had the better of possession in a scrappy opening 20 minutes, but it was an error from Henry that enabled Hughes' side to break the deadlock.
The midfielder allowed the ball to run away from him and Stephen Ireland – in for the injured Bojan Krkic – was quick to pounce and play Walters in with a sumptuous backheel, with the striker making no mistake.
Victor Moses almost doubled their lead three minutes later with a superb free-kick that flew narrowly wide of Robert Green's right-hand post.
Stoke were now in complete control and after 33 minutes another QPR mistake did bring a second goal as Walters broke with Ireland after intercepting Vargas' pass, the Republic of Ireland international holding off three defenders to double his tally.
However, QPR responded well and halved the deficit within three minutes as Kranjcar – starting ahead of Bobby Zamora – tapped home after Charlie Austin's shot had been blocked.
Stoke were forced into a late first-half substitution as Shawcross hobbled off with what looked to be a back injury, with Marc Muniesa replacing him in defence.
Moses wasted two chances to add to Stoke's tally before half-time, and three minutes after the restart Phil Bardsley fired a free-kick inches over the crossbar.
Set-pieces were proving to be the best source of chances after the break with Vargas calling Begovic into action after 56 minutes, the Chilean executing a superb volley from a Leroy Fer free-kick.
Substitute Peter Crouch almost sealed the win for Stoke nine minutes after coming on following a neat passing move, but the striker could not divert Ireland's low cross on target.
Late QPR pressure saw Barton go within a whisker of ending his side's dismal away form after 78 minutes, but his free-kick crashed against the woodwork.
Walters completed his treble in stoppage time with a well-placed header as QPR dallied in defence, ending any hope the visitors had of ending their barren run.
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