Dynamic task-parallel programming models are popular on shared-memory systems, promising enhanced scalability, load balancing and locality. These promises, however, are undermined by non-uniform memory access (NUMA). We show that using NUMA-aware task and data placement, it is possible to preserve the uniform hardware abstraction of contemporary task-parallel programming models for both computing and memory resources with high data locality. Our data placement scheme guarantees that all accesses to task output data target the local memory of the accessing core. The complementary task placement heuristic improves the locality of accesses to task input data on a best effort basis. Our algorithms take advantage of data-flow style task parallelism, where the privatization of task data enhances scalability by eliminating false dependences and enabling fine-grained dynamic control over data placement. The algorithms are fully automatic, application-independent, performance-portable across NUMA machines, and adapt to dynamic changes. Placement decisions use information about inter-task data dependences readily available in the run-time system, and placement information from the operating system. On a 192-core system with 24 NUMA nodes, our optimizations achieve above 94% locality (fraction of local memory accesses), up to 5× better performance than NUMA-aware hierarchical work-stealing, and even 5.6× compared to static interleaved allocation. Finally, we show that state-of-the-art dynamic page migration by the operating system cannot catch up with frequent affinity changes between cores and data and thus fails to accelerate task-parallel applications.