In a single-chip multiprocessor (CMP), the last-level cache and its lower memory hierarchy components are typically shared by multiple processors. Conflicts in these resources lead to poor overall performance of the CMP and/or unpredictable performance of the individual cores. If applications on different cores have different performance constraints, even though these constraints can be satisfied by dynamic voltage and frequency scaling (DVFS) control of each core, conflicts in shared resources will lead to increased power consumption. Therefore, in the present paper, we derive a condition whereby, under resource conflicts, the total power consumption is minimized by a newly developed power consumption model and propose a method by which to minimize the power consumption of CMPs by cooperative access control of multiple shared resources and DVFS control. Experimental results reveal that the proposed technique can reduce power consumption by 15% on average in a dual-core CMP and by 13% in a quad-core CMP, as compared to the case in which only DVFS control is applied.