It was bought by a telephone bidder.
The Constable-Maxwell cage-cup dates from the third century and is decorated with a delicate lattice design. It has survived intact for 17 centuries.
It is the third time the item has set the record for the highest price paid for a piece of ancient glass.
Joanna van der Lande, head of antiquities at Bonhams, said it was likely the glass bowl, thought to have been a grave object, would have originated in the eastern Mediterranean.
Ms van der Lande added: "It's exceptionally fragile and cut from a single block of glass.
"It's something that would have been highly important in its day.
"It would have been clear, but has become iridescent due to a chemical reaction between the earth and the glass.
"Its probable use was as an oil lamp suspended by a metal collar around the rim and light would have come through the lattice work.
"It's really a very highly prized piece."
Roman glass sets auction record
A Roman bowl has become the most expensive piece of ancient glass ever sold at auction. The piece sold for £2,646,650 at Bonhams in London on Wednesday.