Charlie Adam's first goal for Stoke earned his side a 1-0 win against QPR to further increase the pressure on Mark Hughes.
Midfielder Adam, a summer signing from Liverpool, opened his Potters account in the 52nd minute at the Britannia Stadium, tucking the ball away after it had been nodded his way by Jon Walters from a free-kick.
It proved enough to see off QPR, for whom Adel Taarabt failed to convert a good opportunity in the first half.
Both teams looked eager to make an early impression and after QPR full-back Jose Bosingwa had lashed high and wide and Djibril Cisse miscued an attempted volley from an Armand Traore cross, Adam's shot from outside the area deflected wide at the other end.
In the 26th minute Granero tried to dink the ball over the onrushing Begovic, but it only found the side-netting thanks to a combination of the goalkeeper and Matthew Etherington, who picked up an injury and received treatment before playing on.
It was the away side who passed up one of the best chances yet to open the scoring just before the interval, though, when the Potters gave away possession. QPR broke forward and Junior Hoilett squared to Taarabt, who wastefully chipped the ball over.
The Potters went ahead seven minutes after the restart when Robert Huth's free-kick from the left was flicked on by Jonathan Walters, and with QPR failing to react the ball bounced past Peter Crouch and through to Adam, who slammed it home.
The visitors swiftly went in search of a response and Begovic had to be alert to tip over a deflected shot from Taarabt, who then twice dragged the ball across goal from useful positions.
The Moroccan did better in the 70th minute to set up Granero, whose strike brought a great save out of Begovic.