Stripe rust or yellow rust (YR), caused by Puccinia striiformis f. sp. tritici (Pst), is one of the most important diseases of wheat (Triticum aestivum L.). Widespread deployment of resistant cultivars is the best means of achieving durable disease control. The red grain, spring wheat cultivar Napo 63 produced by CIMMYT in the 1960s shows a high level of adult-plant resistance to stripe rust in the field. To elucidate the genetic basis of resistance in this cultivar we evaluated 224 F2:3 lines and 175 F2:6 recombinant inbred lines (RILs) derived from a cross between Napo 63 and the Pst-susceptible line Avocet S. The maximum disease severity (MDS) data of F2:3 lines and the relative area under the disease progress curve (rAUDPC) data of RILs were collected during the 2014–2015 and 2015–2016 wheat growing seasons, respectively. Combined bulked segregant analysis and 90K single nucleotide polymorphism (SNP) arrays placed 275 of 511 polymorphic SNPs on chromosome 2B. Sixty four KASP markers selected from the 275 SNPs and 76 SSR markers on 2B were used to identify a chromosome region associated with rust response. A major effect QTL, named Qyrnap.nwafu-2BS, was identified by inclusive composite interval mapping and was preliminarily mapped to a 5.46 cM interval flanked by KASP markers 90K-AN34 and 90K-AN36 in chromosome 2BS. Fourteen KASP markers more closely linked to the locus were developed following a 660K SNP array analysis. The QTL region was finally narrowed to a 0.9 cM interval flanked by KASP markers 660K-AN21 and 660K-AN57 in bin region 2BS-1-0.53. The resistance of Napo 63 was stable across all environments, and as a QTL, explained an average 66.1% of the phenotypic variance in MDS of F2:3 lines and 55.7% of the phenotypic variance in rAUDPC of F5:6 RILs. The short genetic interval and flanking KASP markers developed in the study will facilitate marker-assisted selection, gene pyramiding, and eventual positional cloning of Qyrnap.nwafu-2BS.