The previous schemes of key establishment in the wireless sensor networks may not be employed for the mission-critical application due to several limitations: lightweightness and scalability from the point of performance, vulnerabilities against node compromise and various existing attacks from the point of security. In this paper, after identifying security requirements of mission-critical applications over sensor networks, we propose a scalable and robust hierarchical key establishment scheme which enhances resilience against node capture, traffic analysis attack and acknowledgment spoofing attack. In addition, our scheme provides periodic key updates without communication costs for key transport. We verified that our scheme requires less storage, computation and communication cost compared with the previous scheme in the open literature. When AES-256 is used for symmetric encryption and one cluster consists of 50 sensor nodes, we can reduce 93.4% storage requirement and 17.2%similar to 51.3% communication cost of the authentication request for the cluster. Since the reduced communication and computation costs enable the time of authentication process to be short, our scheme can support relatively fast initialization and fault recovery. Moreover, our scheme prolongs the lifetime of the wireless sensor networks.