To enable machines to process state-of-practice Web API documentation, we propose a Transformer model for the generic task of identifying a Web API element within a syntax structure that matches a natural language query. We solve this semantic-search task with Transformer-based question answering and demonstrate the applicability of our approach to two different tasks, namely the discovery of endpoints and the identification of parameters in payload schemas. With samples from 2321 OpenAPI documentation, we prepare different datasets and fine-tune pre-trained BERT models to these two tasks. We evaluate the generalizability and the robustness of our fine-tuned models. We achieve accuracies of 81.95% for the parameter-matching and 88.44% for the endpoint-discovery task.