A technique efficiently migrates a live virtual disk (vdisk) across storage containers of a cluster having a plurality of nodes deployed in a virtualization environment. Each node is embodied as a physical computer with hardware resources, such as processor, memory, network and storage resources, that are virtualized to provide support for one or more user virtual machines (UVM) executing on the node. The storage resources include storage devices embodied as a storage pool that is logically segmented into the storage containers configured to store one or more vdisks. The storage containers include a source container having associated storage policies and a destination container having different (new) storage policies. The technique enables migration of the live vdisk from the source container to the destination container without powering down the UVM and halting input/output accesses to the vdisk, and while maintaining uninterrupted servicing of data from the live vdisk during the migration transparent to the executing UVM.