To efficiently support safety-related vehicular applications, the ultra-reliable and low-latency communication (URLLC) concept has become an indispensable component of vehicular networks (VNETs). Due to the high mobility of VNETs, exchanging near-instantaneous channel state information (CSI) and making reliable resource allocation decisions based on such short-term CSI evaluations are not practical. In this paper, we consider the downlink of a vehicle-to-infrastructure (V2I) system conceived for URLLC based on idealized perfect and realistic imperfect CSI. By exploiting the benefits of the massive MIMO concept, a two-stage radio resource allocation problem is formulated based on a novel twin-timescale perspective for avoiding the frequent exchange of near-instantaneous CSI. Specifically, based on the prevalent road-traffic density, Stage 1 is constructed for minimizing the worst-case transmission latency on a long-term timescale. In Stage 2, the base station allocates the total power at a short-term timescale according to the large-scale fading CSI encountered for minimizing the maximum transmission latency across all vehicular users. Then, a primary algorithm and a secondary algorithm are conceived for our V2I URLLC system to find the optimal solution of the twin-timescale resource allocation problem, with special emphasis on the complexity imposed. Finally, our simulation results show that the proposed resource allocation scheme significantly reduces the maximum transmission latency, and it is not sensitive to the fluctuation of road-traffic density.