While supervised relation extraction (RE) models have considerably advanced the state-of-the-art, they often perform poorly in low-resource settings. Zero-shot RE is vital when annotations are not available either due to costs or time constraints. As a result, zero-shot RE has garnered interest in the research community. With the advent of large language models (LLMs) many approaches have been proposed for prompting LLMs for RE, but these methods often either rely on an accompanying small language model (e.g., for finetuning on synthetic data generated by LLMs) or require complex post-prompt processing. In this paper, we propose an effective prompt-based method that does not require any additional resources. Instead, we use an LLM to perform a two-step process. In the first step, we perform a targeted summarization of the text with respect to the underlying relation, reduce the applicable label space, and synthesize examples. Then, we combine the products of these processes with other elements into a final prompt. We evaluate our approach with various LLMs on four real-world RE datasets. Our evaluation shows that our method outperforms the previous state-of-the-art zero-shot methods by a large margin. This work can also be considered as a new strong baseline for zero-shot RE that is compatible with any LLM.