The Chess World Championship, which began on Saturday, sees the world number one and two battle it out for the sport's highest accolade.
The 23-year-old Norwegian, who is favourite to regain his title, lost the game in 34 moves.
Following Tuesday's result in Sochi, it could not be closer with both players tied at 1.5 points each.
After the match, Carlsen's manager Espen Agdestein said: “This wasn't fun, but we have to be prepared to lose. A difficult day and we have to put this behind us as quickly as possible. The challenge is to get this match out of his system.”
But this was the attacking style of play many critics hoped India's 44-year-old Anand would produce against Carlsen.
Carlsen last lost to Anand back in December 2010, and since has kept his grip on being the world's top player.