Introgression of beneficial alleles has emerged as an important avenue for genetic adaptation in both plant and animal populations. In vertebrates, adaptation to hypoxic high-altitude environments involves the coordination of multiple molecular and cellular mechanisms, including selection on the hypoxia-inducible factor (HIF) pathway and the blood-O2 transport protein hemoglobin (Hb). In two Andean duck species, a striking DNA sequence similarity reflecting identity by descent is present across the ~20 kb β-globin cluster including both embryonic (HBE) and adult (HBB) paralogs, though it was yet untested whether this is due to independent parallel evolution or adaptive introgression. In this study, we find that identical amino acid substitutions in the β-globin cluster that increase Hb-O2 affinity have likely resulted from historical interbreeding between high-altitude populations of two different distantly-related species. We examined the direction of introgression and discovered that the species with a deeper mtDNA divergence that colonized high altitude earlier in history (Anas flavirostris) transferred adaptive genetic variation to the species with a shallower divergence (A. georgica) that likely colonized high altitude more recently possibly following a range shift into a novel environment. As a consequence, the species that received these β-globin variants through hybridization might have adapted to hypoxic conditions in the high-altitude environment more quickly through acquiring beneficial alleles from the standing, hybrid-origin variation, leading to faster evolution.