Domain Adaptation (DA), the process of effectively adapting task models learned on one domain, the source, to other related but distinct domains, the targets, with no or minimal retraining, is typically accomplished using the process of source-to-target manifold alignment. However, this process often leads to unsatisfactory adaptation performance, in part because it ignores the task-specific structure of the data. In this paper, we improve the performance of DA by introducing a discriminative discrepancy measure which takes advantage of auxiliary information available in the source and the target domains to better align the source and target distributions. Specifically, we leverage the cohesive clustering structure within individual data manifolds, associated with different tasks, to improve the alignment. This structure is explicit in the source, where the task labels are available, but is implicit in the target, making the problem challenging. We address the challenge by devising a deep DA framework, which combines a new task-driven domain alignment discriminator with domain regularizers that en-courage the shared features as task-specific and domain invariant, and prompt the task model to be data structure preserving, guiding its decision boundaries through the low density data regions. We validate our framework on standard benchmarks, including Digits (MNIST, USPS, SVHN, MNIST-M), PACS, and VisDA. Our results show that our proposal model consistently outperforms the state-of-the-art in unsupervised domain adaptation.