It overshot the previous record of $127m (£83m) set in the same rooms in November 2013 for Francis Bacon's Three Studies of Lucian Freud.
Only a handful of other works are believed to changed hands privately for more including a $300m Gauguin, a $250m Cézanne and a $155m Picasso although the exact details of these deals have not been confirmed.
The 1955 painting appeared in a newly launched evening sale of 20th century art entitled 'Looking Forward to the Past'. The 35-lot sale generated a premium-inclusive $705.85m (£455.4m), making it the second most lucrative auction ever - the record total is Christie's Contemporary art sale in New York in November last year that posted $852.9m (£557.4m) from 80 lots, although this sale had a substantially higher average lot value.
In a night that demonstrated the increased spending power of buyers at the top end of the market, the Christie's sale also recorded the highest auction price for any sculpture as Alberto Giacometti's L'homme au doigt (Pointing Man) took $126m (£85.1m).
Before this sale the record for a Picasso was the $95m (£65.1m) achieved by Nude, Green Leaves and Bust from 1932 also at Christie's in May 2010.
Here, Les femmes d'Alger (Version 'O') was estimated at $140m and was subject to a price guarantee arranged by the auctioneers. Just before the auction began, it was announced from the rostrum that "a party with a financial interest may be bidding" on the lot.
Offered as the eighth lot of the sale, the bidding opened at $100m and, after it quickly rose to $120m, auctioneer Jussi Pylkkänen took it up in increments of $1m with three telephone bidders in contention up to $145m. Two parties carried on beyond this level until the hammer finally fell at $160m to an anonymous telephone buyer bidding through Brett Gorvy, Christie's global head of post-war and contemporary art. There was applause and cheers in the saleroom as the gavel was knocked down.
Homage to Delacroix and Matisse
The work itself was a 3ft 9in x 4ft 10in (1.14 x 1.46m) oil on canvas which was part of a series of 15 works that Picasso based on Delacroix's Les femmes d'Alger (designated as versions A to O). Picasso also conceived the series as a eulogy to Henri Matisse who had died five weeks before he began the series.
Matisse had viewed Delacroix as his immediate forebear in terms of colour and Orientalist subject matter, while Picasso sought to carry this legacy forward, saying: "When Matisse died, he left his odalisques to me as a legacy."
Les femmes d'Alger (Version 'O') was appearing at Christie's 18 years after it last came to auction as part of the landmark sale of the Victor and Sally Ganz collection at Christie's. In November 1997, it was estimated $10-12m and sold at $29m (£17.1m).
The sale of the Ganz collection was a seminal event both for Picasso and the wider market. The auction had five Picassos which fetched over $10m. The $206.5m (£121.5m) premium-inclusive total doubled the previous high for a single-owner auction at the time.
Les femmes d'Alger (Version 'O') was the second highest-selling lot in the sale.
The top lot was Picasso's Le Rêve, a portrait of his mistress Marie-Thérèse Walter which took $44m (£25.8m) - a picture which was later acquired by Steve Wynn in 2001 before the American casino magnate accidentally punctured the canvas with his right elbow in 2006, just after he had agreed to sell it to fellow American collector Steve Cohen for $139m. After it was repaired, Cohen remained interested in the portrait, finally acquiring it from Wynn in a reported $155m deal in 2013.
The performance of Les femmes d'Alger (Version 'O') gave an indication that Picasso's 1950s pictures can now achieve the kind of sums which were previously the reserve of works from the early 1930s. Le Rêve dates from 1932, the same year as Nude, Green Leaves and Bust.
However, with fewer great works from the 1930s now becoming available, collectors have started to show greater interest in works from the artist's later period which are also deemed to have greater crossover appeal to buyers of Contemporary art.
Also at the Christie's sale, Alberto Giacometti's L'homme au doigt (Pointing Man) overshot the record for any sculpture when it sold at $126m (£85.1m). The previous high was the $90m (58.8m) for Giacometti's 1951-52 bronze Chariot that sold at Sotheby's New York in November 2014.
Although the work was offered with an unpublished estimate, it was believed to have been pitched at $130m.
Offered without a guarantee, the earlier bronze from 1947-51 was from an edition of six. It was knocked down to a telephone bidder.
The buyer's premium at Christie's New York was 25/20/12%.
£1 = $1.48