What if Tamerlane the Great had obliterated the Ming Dynasty?

Towards the end of his long and bloody reign of terror throughout Eurasia, Tamerlane the Great received some ambassadors from the newly established Ming Dynasty in China demanding tribute from him. Needless to say, such a request from the Chinese was not a very bright idea at all. It was about as bright as the Fire Inspector who attempted to fine Jewish Bronx gangster Dutch Schultz in the 1930's, and was immediately torn limb from limb by the "Dutchman", for his trouble. Or, as Dutch succinctly put it, "What next, Mailmen?" Tamerlane had actually been unaware of the Ming Dynasty up to that point, and, it would have been much better for them if he had remained that way. Because Tamerlane immediately began planning a full scale invasion of China, and, Tamerlane was rather good at that kind of thing. He'd crushed the Muslims, the Mamluks, the Ottoman Turks, the Mongol Golden Horde etc. etc. etc. All of them, rather more martial and militaristic than the business and administratively oriented Chinese. So, it's rather likely that, had he lived a few years longer, Tamerlane might well have crowned his glorious career of slaughter, theft and carnage with an even more glorious extermination of the Chinese, probably escalating his killing from millions to tens of millions in the heavily populated Chinese empire. So, let's suppose that Tamerlane does live a little longer, and does exterminate the Ming Dynasty, as he might well have done. How, does this change history?