"At the back of the hall, 29 million francs ($31.5 million) — sold!" the Christie's auctioneer said as the fiery almond-shaped gem was snapped up in a room of about 200 people in a luxury hotel.
The price excluded another $4.04 million in taxes and commission.
The man who made the purchase swiftly got up and left the room to a round of applause.
Christie's did not reveal his identity.
The deep orange gemstone, which was found in South Africa, weighs a whopping 14.82 carats.
The Gemological Institute of America (GIA) has handed it the top rating for coloured diamonds: "fancy vivid".
Pure orange diamonds, also known as "fire diamonds", are extremely uncommon and very few have been auctioned, with the largest never more than six carats.
"To have one that's over 14 carats is exceptional," Christie's international jewellery director David Warren told AFP.
He said "The Orange" was "the largest recorded vivid orange diamond in the world".
In 1990, the 4.77-carat yellow-orange Graff Orange diamond was sold for $3.92 million dollars and in 1997 the vivid orange Pumpkin diamond of 5.54 carats was sold for $1.32 million.
Christie's had estimated "The Orange" would rake in $17 million to $20 million.
Rare and expensive 'freaks of nature'
Coloured diamonds, once considered a curiosity, are rarer than white diamonds and today attract higher prices per carat than even the most flawless, translucent stone.
That, Warren explained, was because, "coloured diamonds are real freaks of nature.
They begin as white diamonds, and it's some accidental colouring agent in the ground that will turn it a particular colour."
Green diamonds, for instance, are coloured by radioactivity in the ground, blue diamonds get their colour from boron, and yellow diamonds, which in very rare cases turn orange, are coloured by nitrogen.
Pink diamonds meanwhile get their colour from a distortion in the crystal lattice as the stone is taking shape.
Coloured diamonds "are extraordinarily rare stones," agreed David Bennett, who heads the European jewellery division at Sotheby's.
Christie's rival is set to auction off a flawless 59.60-carat vivid pink diamond, called "The Pink Star", in Geneva on Wednesday, with an asking price of $60 million.
Like "The Orange", the flawless plum-sized shimmering "Pink Star" has received the highest possible colour rating from GIA, as well as top marks for clarity.
It is also the largest of its kind, Bennett said, insisting the anonymous seller was not asking too much.
"Very, very few of these stones have ever appeared at auction and three years ago, a five carat vivid pink made over $10 million.
So the estimate on this stone of $60 million would appear to be very reasonable," he told AFP.
For those who can't cough up that kind of money, both Christie's and Sotheby's "Magnificent Jewels" auctions will also offer a range of other items of historic importance but with lighter price-tags.
There is, for instance, a seven-strand pearl necklace, sold by "a royal family" at an asking price of $4.5 million.
Or the shimmering emerald and diamond necklace by Cartier that has been in the collection of Bolivian tycoon Simon Iturri Patino since he bought it for his wife in 1938.