The network utility maximization problem has wide applications in wireless sensor networks and power grids. In this paper, we propose a distributed event driven optimization method to the network utility maximization problem, which can be regarded as an extension of the classical dual decomposition algorithm. By exploiting the dual problem, we are able to design an active triggering condition on the link side and a passive one on the source side. In particular, the communication triggering logic mediates the information transmission from links to sources. We subsequently present a sufficient condition for the convergence of the flow to the optimal value as well as the reduction of communication frequency. The numerical example verifies that the optimal solution could be achieved distributedly with drastically slashed communication costs.