Scleroderma, or systemic sclerosis (SSc), is an autoimmune disease characterized by progressive fibrosis of the skin and internal organs. The most common cause of death in people with SSc is lung disease, but the pathogenesis of lung disease in SSc is insufficiently understood to devise specific treatment strategies. Developing targeted treatments requires not only the identification of molecular processes involved in SSc-associated lung disease, but also understanding of how these processes interact to drive pathology. One potentially powerful approach is to identify alleles that interact genetically to influence lung outcomes in patients with SSc. Analysis of interactions, rather than individual allele effects, has the potential to delineate molecular interactions that are important in SSc-related lung pathology. However, detecting genetic interactions, or epistasis, in human cohorts is challenging. Large numbers of variants with low minor allele frequencies, paired with heterogeneous disease presentation, reduce power to detect epistasis. Here we present an analysis that increases power to detect epistasis in human genome-wide association studies (GWAS). We tested for genetic interactions influencing lung function and autoantibody status in a cohort of 416 SSc patients. Using Matrix Epistasis to filter SNPs followed by the Combined Analysis of Pleiotropy and Epistasis (CAPE), we identified a network of interacting alleles influencing lung function in patients with SSc. In particular, we identified a three-gene network comprising WNT5A, RBMS3, and MSI2, which in combination influenced multiple pulmonary pathology measures. The associations of these genes with lung outcomes in SSc are novel and high-confidence. Furthermore, gene coexpression analysis suggested that the interactions we identified are tissue-specific, thus differentiating SSc-related pathogenic processes in lung from those in skin.