In this paper, we propose a novel energy-efficient route-discovery scheme with transmission power control (TPC) for ad hoc networks. The proposed scheme is very simple and improves energy efficiency without any information about neighbor nodes. In the proposed scheme, when a node receives a route request (RREQ), the node calculates the routing-level backoff time as being inversely proportional to the received power of the RREQ. After the route discovery, source and intermediate nodes transmit packets by the power-controlled medium access control (MAC) protocol. In addition, we propose an extended version of the proposed scheme for discrete power control devices. Simulation results demonstrate the proposed schemes can discover more energy efficient routes than the conventional schemes.