In this paper, we consider lossy mobile ad hoc networks where the data rate of a given flow becomes lower and lower along its routing path. One of the main challenges in lossy mobile ad hoc networks is how to achieve the conflicting goal of increased network utility and reduced power consumption, while without following the instantaneous state of a fading channel. To address this problem, we propose a cross-layer rate-effective network utility maximization (RENUM) framework by taking into account the lossy nature of wireless links and the constraints of rate outage probability and average delay. In the proposed framework, the utility is associated with the effective rate received at the destination node of each flow instead of the injection rate at the source of the flow. We then present a distributed joint transmission rate, link power and average delay control algorithm, in which explicit broadcast message passing is required for power allocation algorithm. Motivated by the desire of power control devoid of message passing, we give a near-optimal power-allocation scheme that makes use of autonomous SINR measurements at each link and enjoys a fast convergence rate. The proposed algorithm is shown through numerical simulations to outperform other network utility maximization algorithms without rate outage probability/average delay constraints, leading to a higher effective rate, lower power consumption and delay. Furthermore, we conduct extensive network-wide simulations in NS-2 simulator to evaluate the performance of the algorithm in terms of throughput, delay, packet delivery ratio and fairness.