A method includes automatically acquiring, through a resource manager module associated with a driver program executing on a node of a cluster computing system, information associated with utilization of a number of Graphics Processing Units (GPUs associated) with the node, and automatically calculating a window of time in which the node is predictably underutilized on a reoccurring and periodic basis. The method also includes automatically switching off, when one or more GPUs is in an idle state during the window of time, power to the one or more GPUs to transition the one or more GPUs into a quiescent state of zero power utilization thereof. Further, the method includes maintaining the one or more GPUs in the quiescent state until a processing requirement of the node necessitates utilization thereof at a rate higher than a predicted utilization rate of the node during the window of time.