The first major build-up of Antarctic glaciation occurred in two consecutive stages across the Eocene-Oligocene transition (EOT): the EOT-1 cooling event at ~34.1-33.9 Ma and the Oi-1 glaciation event at ~33.8-33.6 Ma. Detailed orbital-scale terrestrial environmental responses to these events remain poorly known. Here we present magnetic and geochemical climate records from the northeastern Tibetan Plateau margin that are dated precisely from ~35.5 to 31 Ma by combined magneto- and astro-chronology. These records suggest a hydroclimate transition at ~33.7 Ma from eccentricity dominated cycles to oscillations paced by a combination of eccentricity, obliquity, and precession, and confirm that major Asian aridification and cooling occurred at Oi-1. We conclude that this terrestrial orbital response transition coincided with a similar transition in the marine benthic δ18O record for global ice volume and deep-sea temperature variations. The dramatic reorganization of the Asian climate system coincident with Oi-1 was, thus, a response to coeval atmospheric CO2 decline and continental-scale Antarctic glaciation.