The enormous proliferation of Internet of Things (IoT) networks necessitates robust and ultra-lightweight authentication mechanisms. Authenticated Encryption with Associated Data (AEAD) schemes are pivotal for resource-constrained devices, but centralized models suffer from a single point of failure. We propose BC-AEAD, a Blockchain-enabled IoT authentication and Authenticated Key Establishment (AKE) scheme using a novel AEAD combiner. BC-AEAD strategically amalgamates the high-performance tweakable block cipher primitive of LOCUS-AEAD with the resource-efficient sponge construction of ASCON. Leveraging Blockchain enables decentralized and tamper-proof key management of the AEAD combiner. The robustness of proposed combiner is validated using an informal security analysis, the Real-and-Random Oracle Model (ROR), and the Scyther tool. The performance of Blockchain network is evaluated regarding throughput, latency, and resource consumption using Hyperledger Caliper v0.4.2. The comparison of computation and communication costs of AKE schemes with state-of-the-art works is accomplished using the Pycrypto toolkit. The cost analysis of BC-AEAD on FPGA proves its practical deployability on highly constrained IoT devices with 1146 LUTs, 428 slices, and 1.86 Gbps. Eventually, the lack of a direct precedent strongly evaluates the core novelty of our unique AEAD combiner.