Hybrid architectures integrating a processor with an SRAM-based FPGA fabric—for example, Xilinx ZynQ SoC—are increasingly being used as a single-chip solution in several market segments to replace multi-chip designs. These devices not only provide advantages in terms of logic density, cost and integration, but also provide run-time in-field reconfiguration capabilities. However, the current reconfiguration capabilities provided by vendor tools are limited to the module level. Therefore, incremental run-time configuration memory changes require a lengthy compilation time for off-line bitstream generation along with storage and reconfiguration time overheads with traditional vendor methodologies. In this paper, an internal configuration access port (ICAP) controller that provides a versatile fine-grain resource-level incremental reconfiguration of the programmable logic (PL) resources in ZynQ SoC is presented. The proposed controller implemented in PL, called VR-ZyCAP, can reconfigure look-up tables (LUTs) and Flip-Flops (FF). The run-time reconfiguration of FF is achieved through a reset after reconfiguration (RAR)-featured partial bitstream to avoid the unintended state corruption of other memory elements. Along with versatility, our proposed controller improves the reconfiguration time by 30 times for FFs compared to state-of-the-art works while achieving a nearly 400-fold increase in speed for LUTs when compared to vendor-supported software approaches. In addition, it achieves competitive resource utilization when compared to existing approaches.