Tanimoto, or (extended) Jaccard, is an important similarity measure which has seen prominent use in fields such as data mining and chemoinformatics. Many of the existing state-of-The-Art methods for market-basket analysis, plagiarism and anomaly detection, compound database search, and ligand-based virtual screening rely heavily on identifying Tanimoto nearest neighbors. Given the rapidly increasing size of data that must be analyzed, new algorithms are needed that can speed up nearest neighbor search, yet provide reliable results. While many search algorithms address the complexity of the task by retrieving only some of the nearest neighbors, we propose a method that finds all of the exact nearest neighbors efficiently by leveraging recent advances in similarity search filtering. We provide tighter filtering bounds for the Tanimoto coefficient and show that our method, TAPNN, greatly outperforms existing baselines across a variety of real-world datasets and similarity thresholds.