In this paper, we show how distributionally-induced semantic classes can be helpful for extracting hypernyms. We present methods for inducing sense-aware semantic classes using distributional semantics and using these induced semantic classes for filtering noisy hypernymy relations. Denoising of hypernyms is performed by labeling each semantic class with its hypernyms. On the one hand, this allows us to filter out wrong extractions using the global structure of distributionally similar senses. On the other hand, we infer missing hypernyms via label propagation to cluster terms. We conduct a large-scale crowdsourcing study showing that processing of automatically extracted hypernyms using our approach improves the quality of the hypernymy extraction in terms of both precision and recall. Furthermore, we show the utility of our method in the domain taxonomy induction task, achieving the state-of-the-art results on a SemEval'16 task on taxonomy induction.