The artist's Self Portrait and his Study for Bullfight No 1, second version, were highlights of Sotheby's evening sale of contemporary art.
His Self Portrait sold for a hammer price of $29.5m (£14.3m) - almost twice the estimate - while his second work in the sale went for $41m (£19.9m).
US artist Jeff Koons' Hanging Heart sculpture was sold for $23.5m (£11.4m).
It established a new record for any living artist's work sold at auction.
Round of applause
The sale gave Sotheby's its highest ever total for an auction of contemporary and postwar art.
Along with a successful contemporary art evening at rival auction house Christie's on Tuesday night, it helped ease fears that the fallout from US credit-market losses had hit the art world.
The concerns were prompted last week when shares in Sotheby's plummeted after a Vincent van Gogh failed to sell.
Bacon's Self Portrait attracted three bidders while five interested parties battled for his Study for Bullfight No 1, second version, which comes from a series of three paintings depicting the subject.
Both sold to a round of applause from the crowded auction room.
Their total value is likely to exceed $80m (£38.9m) once taxes and buyer's fees are added to the hammer price.
Tobias Meyer, Sotheby's worldwide head of contemporary art, said: 'Study for Bullfight No 1 is an extraordinary painting symbolising Bacon wrestling with artistic desire.
'Here, he is battling the demons that occupy his violent subconscious, and in Self Portrait he struggles with these same issues of identity.
'Both masterpieces explore the same conflicts but with different outcomes.'
Text and image by BBC News, UK