Global yields of potato and tomato crops have fallen owing to potato late blight disease, which is caused by Phytophthora infestans. Although most commercial potato varieties are susceptible to blight, many wild potato relatives show variation for resistance and are therefore a potential source of Resistance to P. infestans (Rpi) genes. Resistance breeding has exploited Rpi genes from closely related tuber-bearing potato relatives, but is laborious and slow. Here we report that the wild, diploid non-tuber-bearing Solanum americanum harbors multiple Rpi genes. We combine resistance (R) gene sequence capture (RenSeq) with single-molecule real-time (SMRT) sequencing (SMRT RenSeq) to clone Rpi-amr3i. This technology should enable de novo assembly of complete nucleotide-binding, leucine-rich repeat receptor (NLR) genes, their regulatory elements and complex multi-NLR loci from uncharacterized germplasm. SMRT RenSeq can be applied to rapidly clone multiple R genes for engineering pathogen-resistant crops.