© AP Photos
Set pieces proved to create the best chances of an opening goal in the first period, but strangely it was the Hoops who were the team threatening.
Begovic's opposite number Robert Green was nearly at fault for a Stoke opener when he spilt a Walters shot, only to pounce on the rebound before Crouch, who tested the Hoops shot-stopper with a 25-yard volley, could react to the loose ball.
Crouch beat his former England colleague later in the proceedings, though, converting a cutback from Cameron Jerome after the forward had made a surging run down the left.
Former Rangers striker Crouch was involved again when Stoke doubled their advantage, as Clint Hill impeded him to concede a spot kick, which Walters converted at the second attempt.
QPR's hopes of a late comeback were damaged by injuries to creative duo Taarabt and Andros Townsend, and Stoke saw out the remaining minutes untroubled against a home side 10 points adrift of safety.