The ubiquity of graphics processing unit (GPU) architectures has made them efficient alternatives to chip-multiprocessors for parallel workloads. GPUs achieve superior performance by making use of massive multi-threading and fast context-switching to hide pipeline stalls and memory access latency. However, recent characterization results have shown that general purpose GPU (GPGPU) applications commonly encounter long stall latencies that cannot be easily hidden with the large number of concurrent threads/warps. This results in varying execution time disparity between different parallel warps, hurting the overall performance of GPUs - the warp criticality problem. To tackle the warp criticality problem, we propose a coordinated solution, criticality-aware warp acceleration (CAWA), that efficiently manages compute and memory resources to accelerate the critical warp execution. Specifically, we design (1) an instruction-based and stall-based criticality predictor to identify the critical warp in a thread-block, (2) a criticality-aware warp scheduler that preferentially allocates more time resources to the critical warp, and (3) a criticality-aware cache reuse predictor that assists critical warp acceleration by retaining latency-critical and useful cache blocks in the L1 data cache. CAWA targets to remove the significant execution time disparity in order to improve resource utilization for GPGPU workloads. Our evaluation results show that, under the proposed coordinated scheduler and cache prioritization management scheme, the performance of the GPGPU workloads can be improved by 23% while other state-of-the-art schedulers, GTO and 2-level schedulers, improve performance by 16% and -2% respectively.