Ian Morris calls the Manchu conquest of China the last example of the central Eurasian steppe migration conquering one of the great sedentary societies, although with the difference that the Manchu were already well organized, their army was essentially organized along the lines of a sedentary state, and the new Qing dynasty easily picked up the bureaucratic instruments of the preceding Ming.

Personally speaking, I cannot think of a later example.

The last major invasion of settled society by the American Indian "steppe people" (Great Plains mounted warriors) was probably the "Dakota War" of 1862. In this conflict, the Dakota raided and invaded into Minnesota, killing circa 500 settlers and US soldiers.

The invasion did not last long, however. The Dakota were repulsed in 1862, chased west, and engaged and ultimately defeated in a series of battles in 1863 and 1864.

It is probably more correct to call this a raid, or a minor invasion, rather than a major invasion, but it was one of the strongest and most damaging attacks by the nomadic plains Indians on the encroaching societies of settlers in the history of the American West.

The main cause of the end of the steppe warriors as a major menace to settled societies was the increasing capability of firearms.

Without firearms, the steppe nomads, mounted archers armed with the compound bow, were among the most effective warriors in the world. The steppe societies, however, though they could acquire firearms, did not really have the technological base or infrastructure to produce and re-supply their own firearms and ammunition.

Also, settled societies armed with muskets or rifles, were much more of a match for steppe warriors (even if those warrior were also armed with firearms) than settled societies armed with spears or with crude bows (which they did not practice with much) were against nomads armed with compound bows.

It was with guns that the Russians won the steppes and caused the end of steppe raids on settled societies. It was with guns that settlers drove the American Indian nomads off the plains.

Dan Carlin has a great one part episode on his hardcore history podcast that talks about this. It specifically discusses how throughout history the steppe has periodically released peoples out into the european or eastern asian plains that wreck the settled societies. think of the huns, the mongols, the kipchaks, etc. For a long time, the horse archer was unmatched by the settled societies in what they could offer in terms of mobility and accuracy. All that changed with firearms. And that could be the one word answer to your question, but its still a very good listen. I would recommend checking it out on his website.