The problem of predicting missing links in real-world networks is an active and challenging research area in both science and engineering. The goal is to model the process of link formation in a complex network based on its observed structure to unveil lost or unseen interactions. In this paper, we use perturbation theory to develop a general link prediction procedure, called Laplacian Perturbation Method (LPM), that relies on relevant structural information encoded in the normalized Laplacian matrix of the network. We implement a general algorithm for our perturbation method valid for different Laplacian-based link prediction schemes that successfully surpass the prediction accuracy of their standard non-perturbed versions in real-world and model networks. The suggested LPM for link prediction also exhibits higher accuracy compared to other extensively used local and global state-of-the-art techniques and, in particular, it outperform the Structural Perturbation Method (SPM), a popular procedure that perturbs the adjacency matrix of a network for inferring missing links, in many real-world and in synthetic networks. Taken together, our results show that perturbation methods can significantly improve Laplacian-based link prediction techniques, and feeds the debate on which representation, Laplacian or adjacency, better represents structural information for link prediction tasks in networks.