Mobile edge computing (MEC) has been considered as a promising approach for enabling computation-intensive Internet services in future wireless systems. In this paper, we investigate non-orthogonal multiple access (NOMA) assisted MEC, in which edge-computing users (EUs) adopt NOMA to simultaneously offload part of their computation-workloads to the edge-server (ES). To improve the spectrum-efficiency, we consider a paradigm of underlaying device-to-device (D2D) communications, namely, the EUs reuse a cellular user's (CU's) licensed channel for offloading transmission. We firstly characterize the transmit-powers of EUs and CU in this D2D approach, and then formulate a joint optimization of the EUs' computation- workloads offloading and the ES's computation-resource allocation, with the objective of minimizing the latency in completing the EUs' tasks. In spite of the non-convexity of the formulated problem, we exploit its layered structure and propose an efficient algorithm for computing the optimal solution. Numerical results are provided to validate the effectiveness and efficiency of our proposed NOMA assisted MEC via the D2D sharing.