For multi-homed streaming service, it is important to enhance the throughput by efficient allocation of resources to the most appropriate interfaces of the User Terminal (UT). However, running multiple interfaces simultaneously can significantly contribute to rapid reduction of battery life. In this work, we propose a Power Minimized Rate Allocation Scheme (PMRAS) with optimal rate allocation at each interface with or without packet loss constraint. To develop the PMRAS, we formulate power consumption model based on the network initial interface state (e.g. active or sleep state). To solve convex optimization with multiple constraints, we adopt a Lagrangian algorithm based on dual decomposition. When compared with Rate Proportional additive-increase multiplicative-decrease (AIMD), the proposed algorithm gives significantly reduced total energy consumption with guarantee required Quality of Service (QoS) constraints.