A multiparental random mating population used in sorghum breeding is amenable for the detection of QTLs related to tropical soil adaptation, fine mapping of underlying genes and genomic selection approaches. Tropical soils where low phosphorus (P) and aluminum (Al) toxicity limit sorghum [Sorghum bicolor (L.) Moench] production are widespread in the developing world. We report on BRP13R, a multiparental random mating population (MP-RMP), which is commonly used in sorghum recurrent selection targeting tropical soil adaptation. Recombination dissipated much of BRP13R's likely original population structure and average linkage disequilibrium (LD) persisted up to 2.5 Mb, establishing BRP13R as a middle ground between biparental populations and sorghum association panels. Genome-wide association mapping (GWAS) identified conserved QTL from previous studies, such as for root morphology and grain yield under low-P, and indicated the importance of dominance in the genetic architecture of grain yield. By overlapping consensus QTL regions, we mapped two candidate P efficiency genes to a ~ 5 Mb region on chromosomes 6 (ALMT) and 9 (PHO2). Remarkably, we find that only 200 progeny genotyped with ~ 45,000 markers in BRP13R can lead to GWAS-based positional cloning of naturally rare, subpopulation-specific alleles, such as for SbMATE-conditioned Al tolerance. Genomic selection was found to be useful in such MP-RMP, particularly if markers in LD with major genes are fitted as fixed effects into GBLUP models accommodating dominance. Shifts in allele frequencies in progeny contrasting for grain yield indicated that intermediate to minor-effect genes on P efficiency, such as SbPSTOL1 genes, can be employed in pre-breeding via allele mining in the base population. Therefore, MP-RMPs such as BRP13R emerge as multipurpose resources for efficient gene discovery and deployment for breeding sorghum cultivars adapted to tropical soils.