Most approaches to relation extraction, the task of extracting ground facts from natural language text, are based on machine learning and thus starved by scarce training data. Manual annotation is too expensive to scale to a comprehensive set of relations. Distant supervision, which automatically creates training data, only works with relations that already populate a knowledge base (KB). Unfortunately, KBs such as FreeBase rarely cover event relations (e.g. "person travels to location"). Thus, the problem of extracting a wide range of events --- e.g., from news streams --- is an important, open challenge. This paper introduces NewsSpike-RE, a novel, unsupervised algorithm that discovers event relations and then learns to extract them. NewsSpike-RE uses a novel probabilistic graphical model to cluster sentences describing similar events from parallel news streams. These clusters then comprise training data for the extractor. Our evaluation shows that NewsSpike-RE generates high quality training sentences and learns extractors that perform much better than rival approaches, more than doubling the area under a precision-recall curve compared to Universal Schemas.