In a backbone-assisted industrial wireless network (BAIWN), the technology of successive interference cancellation (SIC) based non-orthogonal multiple access (NOMA) provides potential solutions for improving the delay performance. Previous work emphasizes minimizing the transmission delay by user scheduling without considering power control. However, power control is beneficial for SIC-based NOMA to exploit the power domain and manage co-channel interference to simultaneously serve multiple user nodes with the high spectral and time resource utilization characteristics. In this paper, we consider joint power control and user scheduling to study the scheduling time minimization problem (STMP) with given traffic demands in BAIWNs. Specifically, STMP is formulated as an integer programming problem, which is NP-hard. To tackle the NP-hard problem, we propose a conflict graph-based greedy algorithm, to obtain a sub-optimal solution with low complexity. As a good feature, the decisions of power control and user scheduling can be made by the proposed algorithm only according to the channel state information and traffic demands. The experimental results show that compared with the other methods, the proposed method effectively improves the delay performance regardless of the channel states or the network scales.