Network lifetime is one of the most critical performance measures for wireless sensor networks. Various schemes have been proposed to maximize the network lifetime. In this paper we consider the lifetime maximization problem via a new approach: adaptive power control. We focus on the sensor networks that consists of a sink and a set of homogeneous wireless sensor nodes, which are randomly deployed according to a uniform distribution. Each node has the same initial energy and the same data generation rate. We formally analyze the lifetime maximizing adaptive power control problem by dividing the network into different layers and then modelling it as a linear programming problem, where the goal is to find an optimal way to adjust the transmission power and split the traffic such that the maximum energy consumption speed among all layers is minimized, and therefore the network lifetime is maximized. One surprising observation from the numerical results is that when every node can reach the sink directly, the optimal solution for each node is to send traffic either to its next inner layer or to the sink directly. This observation has also been justified by the theoretical analysis. The numerical results also show that the lifetime elongation can still be significant even when only those nodes in the innermost few layers are allowed to adaptively adjust their transmission power. We then propose a fully distributed algorithm, the Energy-Aware Push Algorithm (EAPA), and show through simulation that it can dramatically extend the network lifetime.