Having lost to Levon Aronian of Armenia in the first round, this turned out to be a double blow for Anand who now finds himself at the last spot in the highest category event.
World champion Magnus Carlsen of Norway played out a draw with Aronian while Fabiano Caruana of Italy hung on to get his draw with Boris Gelfand of Israel in the other games of this six-player round-robin tournament.
With two draws in two games, Caruana is in fourth spot on two points while Gelfand now has one point. Anand is yet to open his account.
Nakamura opted for the Berlin defense as black, a choice of Carlsen in the last world championship match against Anand last year, and got a complicated middle game that favoured Anand.
Not playing the best defense that he is known for, Anand succumbed to the pressure on the king side as Nakamura launched his attack and Anand's two pieces against rook did not prove sufficient. The game lasted 36 moves.