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It is important but challenging to assure the performance of multi-tier Internet applications with the power consumption cap of virtualized server clusters mainly due to system complexity of shared infrastructure and dynamic and bursty nature of workloads. This paper presents PERFUME, a system that simultaneously guarantees power and performance targets with flexible tradeoffs while assuring control accuracy and system stability. Based on the proposed fuzzy MIMO control technique, it accurately controls both the throughput and percentile-based response time of multi-tier applications due to its novel fuzzy modeling that integrates strengths of fuzzy logic, MIMO control and artificial neural network. It is self-adaptive to highly dynamic and bursty workloads due to online learning of control model parameters using a computationally efficient weighted recursive least-squares method. We implement PERFUME in a testbed of virtualized blade servers hosting two multi-tier RUBiS applications. Experimental results demonstrate its control accuracy, system stability, flexibility in selecting tradeoffs between conflicting targets and robustness against highly dynamic variation and burstiness in workloads. It outperforms a representative utility based approach in providing guarantee of the system throughput, percentile-based response time and power budget in the face of highly dynamic and bursty workloads.