A computer system supports a fast hibernation operation to save power, while minimizing the amount of time it takes to enter the hibernation mode, and to resume normal operations. The system periodically stores data from system memory to non-volatile memory, such as a hard disk drive, during normal operations when the system is idle. The system includes activity monitors that detect when the data in memory pages is changed. The system periodically sweeps the monitors, and performs save operations to the non-volatile memory. When the system enters hibernation mode, the system determines which memory pages have been changed since the last save operation, and then saves those pages to memory. As an alternative, the system immediately can enter hibernation by supplying power to the memory pages that have not been saved since the last save operation. To implement this, independent switches under the control of the CPU of memory controller selectively turn off power to unsaved memory pages. The system can also implement a fast resume procedure by restoring the memory pages that have the highest priority, and saving the other pages in the background, or as need by the system devices. Prior to entering the hibernation mode, the pages may be prioritized based on various factors, including the last pages used, the pages used most frequently, or the pages that store the most critical data.