Recent studies suggest that admixture with archaic hominins played an important role in facilitating biological adaptations to new environments. For example, interbreeding with Denisovans facilitated the adaptation to high-altitude environments on the Tibetan Plateau. Specifically, the EPAS1 gene, a transcription factor that regulates the response to hypoxia, exhibits strong signatures of both positive selection and introgression from Denisovans in Tibetan individuals. Interestingly, despite being geographically closer to the Denisova Cave, East Asian populations do not harbor as much Denisovan ancestry as populations from Melanesia. Recently, two studies have suggested two independent waves of Denisovan admixture into East Asians, one of which is shared with South Asians and Oceanians. Here, we leverage data from EPAS1 in 78 Tibetan individuals to interrogate which of these two introgression events introduced the EPAS1 beneficial sequence into the ancestral population of Tibetans, and we use the distribution of introgressed segment lengths at this locus to infer the timing of the introgression and selection event. We find that the introgression event unique to East Asians most likely introduced the beneficial haplotype into the ancestral population of Tibetans around 48,700 (16,000-59,500) y ago, and selection started around 9,000 (2,500-42,000) y ago. Our estimates suggest that one of the most convincing examples of adaptive introgression is in fact selection acting on standing archaic variation.