The emergence of 3D network-on-chip (NoC) has revolutionized the design of high-performance and energy-efficient manycore chips. However, the anticipated performance gain can be compromised due to the degradation and failure of vertical links (VLs). The Through-Silicon-Via (TSV)-enabled VLs may fail due to workload-induced stress; the failure of a VL can affect the neighboring VLs, thereby causing a cascade of failures and reducing the lifetime of the chip. To enhance the reliability of 3D NoC-enabled manycore chips, we propose to incorporate a voltage-frequency island (VFI)-based power management strategy that helps to reduce the energy consumption and hence, the workload-induced stress of the highly utilized VLs. The adopted power-management strategy relies on control decisions about the voltage/frequency (V/F) levels on VLs. We demonstrate that compared to the well-known spare TSV allocation and adaptive routing strategies, power management is more effective in enhancing the reliability of a 3D NoC. VFI-based power management improves the reliability of the 3D NoC by one order of magnitude compared to both adaptive routing and spare allocation while running popular SPLASH-2 and PARSEC benchmarks. The principal benefit of power management is that it is capable of reducing the operating temperature of the system, which in turn enhances the Mean-Time-To-Failure (MTTF) of the VLs and reliability of the overall 3D NoC.