In this paper we propose a low-complexity and effective task mapping, scheduling and power management method for multi-core real-time embedded systems with energy harvesting. The proposed method is based on the concept of task CPU utilization, which is defined as the worst-case task execution time divided by its period. This work mathematically proves that by allocating the new task to the core with the lowest utilization, we can achieve the lowest overall energy dissipation. This method, combined with a new dynamic voltage and frequency selection (DVFS) algorithm with energy harvesting awareness and task slack management (TSM) forms the proposed UTilization Based (UTB) algorithm. With periodical tasks in a multi-core platform, this partitioned scheduling method is optimal for energy dissipation if the proposed utilization-based scheduling and DVFS algorithm is applied on each core. Experimental results show that new algorithm achieves better performance in terms of deadline miss rate in a single-core environment, comparing to the best of existing algorithm. When applied on a multi-core platform, the UTB algorithm achieves better efficiency in utilizing the harvested energy and overflowed energy.