Aegilops mutica (genome T) harbors stripe rust resistance and is a potentially valuable genetic resource for broadening the genetic basis of disease resistance in common wheat. A dominant Ph1-suppression system in Ae. mutica promotes homoeologous pairing and recombination between wheat and alien chromosomes even in the presence of Ph1, providing a tool for alien gene mapping and introgression. In this study, we identified an all-stage stripe rust resistance gene, Yr1T, in Ae. mutica and mapped it to chromosome 1T using chromosome deletion lines of Langdon × Ae. mutica amphidiploids. Genetic stocks with an AABBTD genomic constitution were generated by crossing resistant amphidiploids with the susceptible common wheat cultivar MX169. We induced homoeologous recombination between chromosome 1T and wheat homoeologous group 1 chromosomes by leveraging the Ae. mutica Ph1-suppression system. Integrating cytological identification, molecular markers, and RNA-seq breakpoint mapping, Yr1T was delimited to an approximately 20 Mb physical interval near the centromere in chromosome arm 1TS. Screening of a 100-plant F₂ population yielded six recombinant plants with different breakpoints (6% recombination frequency), and a translocation line carrying Yr1T was developed. Collectively, these results demonstrated the high efficiency of the Ae. mutica Ph1-suppression system for alien gene mapping and targeted transfer, providing a practical reference for its application in wheat breeding.