[obligatory complaint about how western-centric this list is]
I agree. There is probably quite a number of Chinese-Mongolian battles to add, as well as stuff about Central Asia (Tamerlane-> Islamising Afghanistan & Pakistan, weakening the Golden Horde which ultimately allowed for Russian expansion into Siberia, etc.). Unfortunately, people in the West (including myself) are not very knowledgeable in this respect. Any effort to close such knowledge gaps is highly appreciated!
The Battle of the Talas River (the early Caliphate defeated Tang China and, while not pressing forward into the Empire proper, broke Chinese hegemony in Central Asia), the Battle of Ayn Jalut (the Mongol high-water-mark in the Levant), the Battle of Dan-no-ura (the Minamoto clan defeated the Taira clan for control of Japan, ending the Heian period--Japan's closest analogue of Classical Antiquity, basically--and the near-complete dominance of the samurai), the Battle of Yamen (the final defeat of Song China and the solidification of Kublai Khan's power in one of the largest naval battles in history--the Mongol fleet routed a Song fleet ten times its size), the Battle of Chuvash Cape (the first decisive Russian victory in the conquest of Siberia), the Battle of Hansan Island (Joseon Korea defeated Toyotomi Hideyoshi's Japanese force in
another of the largest naval battles in history, stimying a conceived--though perhaps unrealistically so all along--Japanese conquest of both Korea and China), and the Battles of Geok Tepe (a Turkmen group defeated an expeditionary force from Tsarist Russia, which then conquered much of Central Asia in a retaliatory strike two years later) all come to mind from pre-modern/early modern Asian history.