Analysis of lunar rocks brought back by the Apollo missions shows they have heavier forms of zinc - a telltale sign of the impact billions of years ago.
Without the Moon, there may have been no life on Earth because it once orbited much closer to us than it does now causing massive tides to ebb and flow every few hours.
These tides caused dramatic fluctuations in salinity around coastlines which are believed to have driven the evolution of primitive DNA-like biomolecules.
Researchers led by Dr Frederic Moynier from Washington University said the zinc enrichment probably arose because heavier atoms condensed out of the cloud of vapourised rock quicker than lighter ones.
Researchers analysed 20 samples of Moon rocks including ones from the Apollo 11, 12, 15 and 17 missions and one lunar meteorite.
"What we wanted were the basalts because they're the ones that came from inside the Moon and would be more representative of the Moon's composition," Moynier, said.
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Scientists have been looking for this kind of sorting by mass - called isotopic fractionation - since the Apollo missions first brought Moon rocks to Earth in the 1970s.
Compared to terrestrial or Martian rocks, the lunar rocks have much lower concentrations of zinc but are enriched in the heavy isotopes of zinc.
"The magnitude of the fractionation we measured in lunar rocks is 10 times larger than what we see in terrestrial and Martian rocks, so it's an important difference," Moynier said.
Earth and Mars have isotopic compositions like those of chondritic meteorites, which are thought to represent the original composition of the cloud of gas and dust from which the solar system formed.
The most likely large-scale event is wholesale melting during the formation of the Moon.
The zinc isotopic data therefore supports the theory a giant impact gave rise to the Earth-Moon system.
"The work also has implications for the origin of the Earth because the origin of the Moon was a big part of the origin of the Earth," Moynier said in a statement.
Without the stabilising influence of the Moon, the Earth would probably be a very different sort of place.
Scientists believe the Earth would spin more rapidly, days would be shorter, weather more violent and climate more chaotic and extreme.
The study findings are published in the journal Nature.