The bag, auctioned on the occasion of the 48th anniversary of mankind's first moon landing, was expected to fetch an amount between US $2-4 million. It still contains traces of the moon dust, Sotheby's said.
During the Apollo 11 mission in 1969, Mr Armstrong collected nearly 500 grammes of material finer than one centimetre, as well as 12 rock fragments larger than a centimetre from five different locations on the lunar surface in the region known as the Sea of Tranquility.
Given the then unknown nature of lunar material, the decontamination bag was used to minimise any potential harm the samples might pose to the Command Module and planet Earth.
Nearly all of the equipment from that historic mission is housed in the US National Collections at the Smithsonian; however a recent court ruling has allowed this to be the only such artefact in private hands.
The true history of the bag went unknown for decades until just a year ago.
It was offered three separate times in 2014 by a small auction house on behalf of the US Marshall's service, garnering not a single bid.
It was re-listed in 2015, where it was sold for US $995.
Scientific tests at NASA revealed the dust in the bag to be moon dust, specifically from the Apollo 11 landing site, and the part number printed inside of the bag matched up to that of the "Contingency Lunar Sample Return Decontamination Bag" listed in the Apollo 11 Stowage list.
"Reflecting the enduring and universal fascination with space, the US $1.8 million achieved for the Apollo 11 lunar sample bag and strong prices for objects related to other missions were driven by over 500 participants from dozens of countries with many buyers new to Sotheby's," said Cassandra Hatton, Vice President and Senior Specialist of Sotheby's Books and Manuscripts Department in New York.
In addition to the Apollo 11 lunar bag, early space photography by noteworthy astronomers and NASA innovations obtained substantial prices while American painter Chesley Bonestell's artistic interpretations of space flew high above expectations.
In particular, "Stone Architecture on Mars, Demonstrating Mars' two-thirds less gravity than Earth's" sold for US $125,000, over twelve times its high estimate.
Materials from the Soviet space missions drew bids online and on the telephone while a Snoopy Astronaut Doll, Mascot of the Apollo 10 LM Crew, was sold for US $27,500.
One of the final lots of the sale also found significant interest in the auction room this afternoon.
The Flown Apollo 13 Flight Plan, with handwritten notations by all three crew members following the onboard explosion, was sold to an online bidder for US $275,000.