Pansharpening is a crucial and challenging task that aims to obtain a high spatial resolution image by merging a multispectral (MS) image and a panchromatic (PAN) image. Current methods use CNNs with standard convolution, but we've observed strong correlation among channel dimensions in the kernel, leading to computational burden and redundancy. To address this, we propose Learnable Gaussian Perturbation Convolution (LGPConv), surpassing standard convolution. LGPConv leverages two properties of standard convolution kernels: 1) correlations within channels, learning a premier kernel as a base to reduce parameters and training difficulties caused by redundancy; 2) introducing Gaussian noise perturbations to simulate randomness and enhance nonlinear representation within channels. We incorporate LGPConv into a well-designed pansharpening network and demonstrate its superiority through extensive experiments, achieving state-of-the-art performance with minimal parameters (27K). Code is available on the GitHub page of the authors.