This work addresses unsupervised partial domain adaptation (PDA), in which classes in the target domain are a subset of the source domain. The key challenges of PDA are how to leverage source samples in the shared classes to promote positive transfer and filter out the irrelevant source samples to mitigate negative transfer. Existing PDA methods based on adversarial DA do not consider the loss of class discriminative representation. To this end, this article proposes a contrastive learning-assisted alignment (CLA) approach for PDA to jointly align distributions across domains for better adaptation and to reweight source instances to reduce the contribution of outlier instances. A contrastive learning-assisted conditional alignment (CLCA) strategy is presented for distribution alignment. CLCA first exploits contrastive losses to discover the class discriminative information in both domains. It then employs a contrastive loss to match the clusters across the two domains based on adversarial domain learning. In this respect, CLCA attempts to reduce the domain discrepancy by matching the class-conditional and marginal distributions. Moreover, a new reweighting scheme is developed to improve the quality of weights estimation, which explores information from both the source and the target domains. Empirical results on several benchmark datasets demonstrate that the proposed CLA outperforms the existing state-of-the-art PDA methods.