Maintaining peer-to-peer connectivity with low energy overhead is a key requirement for several emerging Internet of Things (IoT) applications. It is also desirable to develop such connectivity solutions for non-static network topologies, so that resilience to device failures can be fully realized. Decentralized clustering has emerged as a promising technique to address this critical challenge. Clustering of nodes around cluster heads (CHs) provides an energy-efficient two-tier framework for peer-to-peer communication. At the same time, decentralization ensures that the framework can quickly adapt to a dynamically changing network topology. Although some decentralized clustering solutions have been proposed in the literature, they either lack guarantees on connectivity or incur significant energy overhead to maintain the clusters. In this paper, we present Decentralized Connected Resilient IoT Clustering (DeCoRIC), an energy-efficient clustering scheme that is self-organizing and resilient to network changes while guaranteeing connectivity. Using experiments implemented on the Contiki simulator, we show that our clustering scheme adapts itself to node faults in a time-bound manner. Our experiments show that DeCoRIC achieves 100% connectivity among all nodes while improving the power efficiency of nodes in the system compared to the state-of-the-art techniques BEEM and LEACH by up to 110% and 70%, respectively. The improved power efficiency also translates to longer lifetime before first node death with a best-case of 109% longer than BEEM and 42% longer than LEACH.