Massively multithreaded GPUs achieve high throughput by running thousands of threads in parallel. To fully utilize the hardware, contemporary workloads spawn work to the GPU in bulk by launching large tasks, where each task is a kernel that contains thousands of threads that occupy the entire GPU. GPUs face severe underutilization and their performance benefits vanish if the tasks are narrow, i.e., they contain less than 512 threads. Latency-sensitive applications in network, signal, and image processing that generate a large number of tasks with relatively small inputs are examples of such limited parallelism. Recognizing the issue, CUDA now allows 32 simultaneous tasks on GPUs; however, that still leaves significant room for underutilization. This paper presents Pagoda, a runtime system that virtualizes GPU resources, using an OS-like daemon kernel called MasterKernel. Tasks are spawned from the CPU onto Pagoda as they become available, and are scheduled by the MasterKernel at the warp granularity. This level of control enables the GPU to keep scheduling and executing tasks as long as free warps are found, dramatically reducing underutilization. Experimental results on real hardware demonstrate that Pagoda achieves a geometric mean speedup of 2.44x over PThreads running on a 20-core CPU, 1.43x over CUDA-HyperQ, and 1.33x over GeMTC, the state-of-the-art runtime GPU task scheduling system.