The long-standing goal of dense retrievers in abtractive open-domain question answering (ODQA) tasks is to learn to capture evidence passages among relevant passages for any given query, such that the reader produce factually correct outputs from evidence passages. One of the key challenge is the insufficient amount of training data with the supervision of the answerability of the passages. Recent studies rely on iterative pipelines to annotate answerability using signals from the reader, but their high computational costs hamper practical applications. In this paper, we instead focus on a data-driven approach and propose Evidentiality-Aware Dense Passage Retrieval (EADPR), which leverages synthetic distractor samples to learn to discriminate evidence passages from distractors. We conduct extensive experiments to validate the effectiveness of our proposed method on multiple abstractive ODQA tasks.