City dominated from first to last and Higginbotham struck the crucial blow from the penalty spot after Mauro Milanese had fouled Ricardo Fuller.
Prior to that 18th-minute goal Fuller and Lee Hendrie had had early chances.
There was to be no let up with Mamady Sidibe, Darel Russell and Hendrie going close, while in defence Stoke have now gone 656 minutes without conceding.
QPR boss John Gregory was unhappy with the match-winning penalty:
"I didn't think it was a penalty, but the referee was quick to point to the spot and I'll have to see the tape to be sure. "We had to reshuffle our pack and I thought the players we put out there did well."
Stoke: Simonsen, Hoefkens, Duberry, Higginbotham, Griffin, Lawrence, Diao (Brammer 80), Russell, Hendrie (Berger 87), Sidibe, Fuller (Pericard 74).
Subs Not Used: Sweeney, Buxton.
Booked: Griffin.
Goals: Higginbotham 17 pen.
QPR: Royce, Bignot, Mancienne, Stewart, Milanese, Rowlands (Ward 87), Bailey, Gallen, Smith, Nygaard (Baidoo 90), Blackstock (Furlong 70).
Subs Not Used: Cole, Bircham.
Booked: Mancienne.
Att: 16,487
Ref: M Atkinson (W Yorkshire).
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