Modern user facing applications consist of multiple processing stages with a number of service instances in each stage. The latency profile of these multi-stage applications is intrinsically variable, making it challenging to provide satisfactory responsiveness. Given a limited power budget, improving the end-to-end latency requires intelligently boosting the bottleneck service across stages using multiple boosting techniques. However, prior work fail to acknowledge the multi-stage nature of user-facing applications and perform poorly in improving responsiveness on power constrained CMP, as they are unable to accurately identify bottleneck service and apply the boosting techniques adaptively. In this paper, we present PowerChief, a runtime framework that 1) provides joint design of service and query to monitor the latency statistics across service stages and accurately identifies the bottleneck service during runtime; 2) adaptively chooses the boosting technique to accelerate the bottleneck service with improved responsiveness; 3) dynamically reallocates the constrained power budget across service stages to accommodate the chosen boosting technique. Evaluated with real world multi-stage applications, PowerChief improves the average latency by 20.3脳 and 32.4脳 (99% tail latency by 13.3脳 and 19.4脳) for Sirius and Natural Language Processing applications respectively compared to stage-agnostic power allocation. In addition, for the given QoS target, PowerChief reduces the power consumption of Sirius and Web Search applications by 23% and 33% respectively over prior work.