Web servers service client requests, some of which might cause the web server to perform security-sensitive operations (e.g. money transfer, voting). An attacker may thus forge or maliciously manipulate such requests by compromising a web client. Unfortunately, a web server has no way of knowing whether the client from which it receives a request has been compromised or not -- current "best practice" defenses such as user authentication or network encryption cannot aid a server as they all assume web client integrity. To address this shortcoming, we propose vWitness, which "witnesses" the interactions of a user with a web page and certifies whether they match a specification provided by the web server, enabling the web server to know that the web request is user-intended. The main challenge that vWitness overcomes is that even benign clients introduce unpredictable variations in the way they render web pages. vWitness differentiates between these benign variations and malicious manipulation using computer vision, allowing it to certify to the web server that 1) the web page user interface is properly displayed 2) observed user interactions are used to construct the web request. Our vWitness prototype achieves compatibility with modern web pages, is resilient to adversarial example attacks and is accurate and performant -- vWitness achieves 99.97% accuracy and adds 197ms of overhead to the entire interaction session in the average case.