In many real-world settings, the critical class is rare and a missed detection carries a disproportionately high cost. For example, tumors are rare and a false negative diagnosis could have severe consequences on treatment outcomes; fraudulent banking transactions are rare and an undetected occurrence could result in significant losses or legal penalties. In such contexts, systems are often operated at a high true positive rate, which may require tolerating high false positives. In this paper, we present a novel approach to address the challenge of minimizing false positives for systems that need to operate at a high true positive rate. We propose a ranking-based regularization (RankReg) approach that is easy to implement, and show empirically that it not only effectively reduces false positives, but also complements conventional imbalanced learning losses. With this novel technique in hand, we conduct a series of experiments on three broadly explored datasets (CIFAR-10&100 and Melanoma) and show that our approach lifts the previous state-of-the-art performance by notable margins.