Modern grid codes demand the integration of voltage support capability with photo-voltaic (PV) generators to ensure a secure and reliable grid operation. On the other hand, short-term voltage instability (STVI) of distribution networks (DNs) is one of the key issues to be addressed due to the rising proportion of induction motor (IM) loads. However, the literature lacks an extensive analysis of short-term voltage stability (STVS) following an unsymmetrical fault in a DN, as well as an effective voltage-support strategy for PV units to improve the STVS while mitigating the excessive voltage swell. Therefore, at first, this paper thoroughly investigates the STVS of a DN subjected to an unbalanced fault. It is perceived that voltage support through conventional methods can increase the risk of STVI and excessive voltage swell. Secondly, a new voltage-support strategy is proposed based on the negative sequence voltage at the point of common coupling (PCC) to improve the STVS and to limit the voltage swell within requirement. The key features of the proposed method are (1) fast and accurate estimation of a network's impedance at PCC is not required, and (2) can be re-designed considering the network behaviors. The proposed method is validated on two IEEE benchmark test systems, and the provided results designate the effectiveness in improving the STVS and alleviating over voltage issues in a DN.