Antibiotic-resistant infections kill approximately 23,000 people and cost $20,000,000,000 each year in the United States alone despite the widespread use of small-molecule antimicrobial combination therapy. Antibiotic combinations typically have an additive effect: the efficacy of the combination matches the sum of the efficacies of each antibiotic when used alone. Small molecules can also act synergistically when the efficacy of the combination is greater than the additive efficacy. However, synergistic combinations are rare and have been historically difficult to identify. High-throughput identification of synergistic pairs is limited by the scale of potential combinations: a modest collection of 1,000 small molecules involves 1 million pairwise combinations. Here, we describe a high-throughput method for rapid identification of synergistic small-molecule pairs, the overlap2 method (O2M). O2M extracts patterns from chemical-genetic datasets, which are created when a collection of mutants is grown in the presence of hundreds of different small molecules, producing a precise set of phenotypes induced by each small molecule across the mutant set. The identification of mutants that show the same phenotype when treated with known synergistic molecules allows us to pinpoint additional molecule combinations that also act synergistically. As a proof of concept, we focus on combinations with the antibiotics trimethoprim and sulfamethizole, which had been standard treatment against urinary tract infections until widespread resistance decreased efficacy. Using O2M, we screened a library of 2,000 small molecules and identified several that synergize with the antibiotic trimethoprim and/or sulfamethizole. The most potent of these synergistic interactions is with the antiviral drug azidothymidine (AZT). We then demonstrate that understanding the molecular mechanism underlying small-molecule synergistic interactions allows the rational design of additional combinations that bypass drug resistance. Trimethoprim and sulfamethizole are both folate biosynthesis inhibitors. We find that this activity disrupts nucleotide homeostasis, which blocks DNA replication in the presence of AZT. Building on these data, we show that other small molecules that disrupt nucleotide homeostasis through other mechanisms (hydroxyurea and floxuridine) also act synergistically with AZT. These novel combinations inhibit the growth and virulence of trimethoprim-resistant clinical Escherichia coli and Klebsiella pneumoniae isolates, suggesting that they may be able to be rapidly advanced into clinical use. In sum, we present a generalizable method to screen for novel synergistic combinations, to identify particular mechanisms resulting in synergy, and to use the mechanistic knowledge to rationally design new combinations that bypass drug resistance.