Recent studies have shown that cooperative multi-agent deep reinforcement learning (c-MADRL) is under the threat of backdoor attacks. Once a backdoor trigger is observed, it will perform malicious actions leading to failures or malicious goals. However, existing backdoor attacks suffer from several issues, e.g., instant trigger patterns lack stealthiness, the backdoor is trained or activated by an additional network, or all agents are backdoored. To this end, in this paper, we propose a novel backdoor leverage attack against c-MADRL, BLAST, which attacks the entire multi-agent team by embedding the backdoor only in a single agent. Firstly, we introduce adversary spatiotemporal behavior patterns as the backdoor trigger rather than manual-injected fixed visual patterns or instant status and control the period to perform malicious actions. This method can guarantee the stealthiness and practicality of BLAST. Secondly, we hack the original reward function of the backdoor agent via unilateral guidance to inject BLAST, so as to achieve the \textit{leverage attack effect} that can pry open the entire multi-agent system via a single backdoor agent. We evaluate our BLAST against 3 classic c-MADRL algorithms (VDN, QMIX, and MAPPO) in 2 popular c-MADRL environments (SMAC and Pursuit), and 2 existing defense mechanisms. The experimental results demonstrate that BLAST can achieve a high attack success rate while maintaining a low clean performance variance rate.