This paper studies a novel channel access scheme for delay-sensitive multi-hop cognitive radio sensor networks (CRSNs) with fixed decode-and-forward relaying. We first formulate a two-dimensional spatial-temporal opportunity model wherein free and sharing opportunities are defined, and then propose a joint spatial-temporal access scheme (JSTAS) to achieve successive channel access for continuous data transmission. By spatial sensing and temporal sensing, the cognitive sensors with JSTAS control the transmission powers by fully considering their maximum transmission powers, the interference constraints of multiple primary receivers and the interference from one primary transmitter. To evaluate JSTAS, we derive the closed-form outage probability under Rayleigh fading channels and make comparisons among five different schemes. Simulation results demonstrate that JSTAS has better outage performance than that of pure spatial or temporal access scheme under all considered scenarios.