The proliferation of mobile devices and ubiquitous access of the wireless network enables many new mobile applications such as augmented reality, mobile gaming and so on. As the applications are latency sensitive, researchers propose to offload the complex computations of these applications to the nearby mobile edge cloud, in order to reduce the latency. Existing works mostly consider the problem of partitioning the computations between the mobile device and the traditional cloud that has abundant resources. The proposed approaches can not be applied in the context of mobile edge cloud, because both the resources in the mobile edge cloud and the wireless access bandwidth to the edge cloud are constrained. In this paper, we study joint computation partitioning and resource allocation problem for latency sensitive applications in mobile edge clouds. The problem is novel in that we combine the computation partitioning and the two-dimensional resource allocations in both the computation resources and the network bandwidth. We develop a new and efficient method, namely Multi-Dimensional Search and Adjust (MDSA), to solve the problem. We compares MDSA with the classic list scheduling method and the SearchAdjust algorithm via comprehensive simulations. The results show that MDSA outperforms the benchmark algorithms in terms of the overall application latency.