Recent research efforts have explored the potential of leveraging natural language inference (NLI) techniques to enhance relation extraction (RE). In this vein, we introduce MetaEntail-RE, a novel adaptation method that harnesses NLI principles to enhance RE performance. Our approach follows past works by verbalizing relation classes into class-indicative hypotheses, aligning a traditionally multi-class classification task to one of textual entailment. We introduce three key enhancements: (1) Instead of labeling non-entailed premise-hypothesis pairs with the uninformative "neutral" entailment label, we introduce meta-class analysis, which provides additional context by analyzing overarching meta relationships between classes when assigning entailment labels; (2) Feasible hypothesis filtering, which removes unlikely hypotheses from consideration based on pairs of entity types; and (3) Group-based prediction selection, which further improves performance by selecting highly confident predictions. MetaEntail-RE is conceptually simple and empirically powerful, yielding significant improvements over conventional relation extraction techniques and other NLI formulations. Our experimental results underscore the versatility of MetaEntail-RE, demonstrating performance gains across both biomedical and general domains.