Nvidia Tensor Cores achieve high performance with half-precision matrix inputs tailored towards deep learning workloads. However, this limits the application of Tensor Cores especially in the area of scientific computing with high precision requirements. In this paper, we build Emulated GEMM on Tensor Cores (EGEMM-TC) to extend the usage of Tensor Cores to accelerate scientific computing applications without compromising the precision requirements. First, EGEMM-TC employs an extendable workflow of hardware profiling and operation design to generate a lightweight emulation algorithm on Tensor Cores with extended-precision. Second, EGEMM-TC exploits a set of Tensor Core kernel optimizations to achieve high performance, including the highly-efficient tensorization to exploit the Tensor Core memory architecture and the instruction-level optimizations to coordinate the emulation computation and memory access. Third, EGEMM-TC incorporates a hardware-aware analytic model to offer large flexibility for automatic performance tuning across various scientific computing workloads and input datasets. Extensive evaluations show that EGEMM-TC can achieve on average 3.13X and 11.18X speedup over the cuBLAS kernels and the CUDA-SDK kernels on CUDA Cores, respectively. Our case study on several scientific computing applications further confirms that EGEMM-TC can generalize the usage of Tensor Cores and achieve about 1.8X speedup compared to the hand-tuned, highly-optimized implementations running on CUDA Cores.