Image harmonization aims to modify the color of the composited region according to the specific background. Previous works model this task as a pixel-wise image translation using UNet family structures. However, the model size and computational cost limit the ability of their models on edge devices and higher-resolution images. In this paper, we propose spatial-separated curve rendering network (S CRNet), a novel framework to prove that the simple global editing can effectively address this task as well as the challenge of high-resolution image harmonization for the first time. In S CRNet, we design a curve rendering module (CRM) using spatial-specific knowledge to generate the parameters of the piece-wise curve mapping in the foreground region and we can directly render the original high-resolution images using the learned color curve. Besides, we also make two extensions of the proposed framework via cascaded refinement and semantic guidance. Experiments show that the proposed method reduces more than 90% parameters compared with previous methods but still achieves the state-of-the-art performance on 3 benchmark datasets. Moreover, our method can work smoothly on higher resolution images with much lower GPU computational resources. The source codes are available at: http://github.com/stefanLeong/S2CRNet.