We develop a probabilistic approach for accurate network modeling using node popularities within the framework of the mixed-membership stochastic blockmodel (MMSB). Our model integrates some of the basic properties of nodes in social networks: homophily and preferential connection to popular nodes. We develop a scalable algorithm for posterior inference, based on a novel nonconjugate variant of stochastic variational inference. We evaluate the link prediction accuracy of our algorithm on eight real-world networks with up to 60,000 nodes, and 24 benchmark networks. We demonstrate that our algorithm predicts better than the MMSB. Further, using benchmark networks we show that node popularities are essential to achieving high accuracy in the presence of skewed degree distribution and noisy links---both characteristics of real networks.