Bandwidth aggregation (BAG) techniques have been researched for many years in an efforts to enhance throughput for multi-homed streaming service. However, despite of the considerable attention being devoted towards energy-efficient communications, the power efficiency for BAG has not been considered yet. To improve the power efficiency in multi-homed streaming service, this paper proposes Power Minimized Rate Allocation Scheme (PMRAS) with optimal rate allocation at each interface while guaranteeing an allowable packet loss rate. In developing PMRAS, we first formulate a power consumption model based on the network interface state (i.e. active and idle state). We adopt a Lagrangian algorithm to solve the convex optimization problem of power consumption. The performance results gained from a numerical analysis and simulations (NS-2) reveal that the proposed scheme offers superior performance over the existing rate allocation scheme for BAG with guaranteed required quality of service.