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Genome-wide association (GWA) studies typically lack power to detect genotypes significantly associated with complex diseases, where different causal mutations of small effect may be present across cases. A common, tractable approach for identifying genomic elements associated with complex traits is to evaluate combinations of variants in known pathways or gene sets with shared biological function. Such gene-set analyses require the computation of gene-level P-values or gene scores; these gene scores are also useful when generating hypotheses for experimental validation. However, commonly used methods for generating GWA gene scores are computationally inefficient, biased by gene length, imprecise, or have low true positive rate (TPR) at low false positive rates (FPR), leading to erroneous hypotheses for functional validation. Here we introduce a new method, PEGASUS, for analytically calculating gene scores. PEGASUS produces gene scores with as much as 10 orders of magnitude higher numerical precision than competing methods. In simulation, PEGASUS outperforms existing methods, achieving up to 30% higher TPR when the FPR is fixed at 1%. We use gene scores from PEGASUS as input to HotNet2 to identify networks of interacting genes associated with multiple complex diseases and traits; this is the first application of HotNet2 to common variation. In ulcerative colitis and waist–hip ratio, we discover networks that include genes previously associated with these phenotypes, as well as novel candidate genes. In contrast, existing methods fail to identify these networks. We also identify networks for attention-deficit/hyperactivity disorder, in which GWA studies have yet to identify any significant SNPs.