Android apps could expose their components for cooperating with other apps. This convenience, however, makes apps susceptible to the exposed component vulnerability (ECV), in which a dangerous API (commonly known as sink) inside its component can be triggered by other (malicious) apps. In the prior works, detecting these ECVs use a set of sinks pertaining to the ECVs under detection. In this paper, we argue that a more comprehensive and effective approach should start by a systematic selection and classification of vulnerability-specific sinks (VSinks). The set of VSinks is much larger than those used in the previous works. Based on these VSinks, our sink-driven approach can detect different kinds of ECVs in an app in two steps. First, VSinks and their categories are identified through a typical forward reachability analysis. Second, based on each VSink's category, a corresponding detection method is used to identify the ECV via a customized backward dataflow analysis. We also design a semi-auto guided analysis and validation capability for system-only broadcast checking to remove some false positives. We implement our sink-driven approach in a tool called ECVDetector and evaluate it with the top 1K Android apps. Using ECVDetector we successfully identify a total of 49 vulnerable apps across all four ECV categories we have defined. To our knowledge, most of them are previously undisclosed, such as the very popular Go SMS Pro and Clean Master. Moreover, the performance of ECVDetector is high, requiring only 9.257 seconds on average to process each component.