The most obvious example is, I think, the collapse of the Western Roman Empire largely as the result of invasion by Germanic tribes in the 5th Century, C.E. There is some argument that the Empire collapsed under its own weight; however the role of the various Germanic tribes, including the Goths, Vandals and Franks, together with the pressure from the Huns, cannot be underestimated. Rome was at the time the most advanced civilization in the world, and had built a tremendous Empire. The Empire was brought to its knees by warriors from an illiterate society that had few if any cities and were commonly called "barbarian" by the Romans because their spoken language resembled the noise of bleating sheep. Rome itself was invaded by the Goths, and ultimately a Visigothic Chieftain, Odoacher, deposed the last remaining Western Emperor, thus putting an end to that Empire forever.
There are many examples of this, though we would need to define what exactly "defeated" means. A recent example would be the Soviet invasion of Afghanistan. After a long and bloody conflict spanning a decade, Afghan fighters, as well as foreign mujahideen, Soviet troops withdrew, having failed to fulfill their mission of propping up a communist government in the country. However, the Soviets did inflict horrible casualties on the Afghan people, and Afghan resistance was bolstered both by foreign fighters and by billions of dollars in American military aid, so pointing to the conflict as an unqualified Afghan victory is problematic. In human terms, it was a disaster. One might also point to the United States' involvement in Vietnam as an example of a victory for a less materially advanced society over a major power, though some of the same qualifiers would apply as in Afghanistan.
Mongol conquest of China 13th century
Arab conquest of Persia and much of Byzantium in 7th century
Probably, Aztec conquest of Mexico in the fifteenth century, although historians might not agree.
Scythian and Aryan invasions of Middle East and India.
Hyksos invasion of Egypt
Goths conquest of Rome
Hebrews conquest of Canaan
Persian conquest of Babylon