The much awaited clash turned out to be a full entertainer to the audience as Carlsen tried but could not make much use of his white pieces in a keenly contested game arising out of a Sicilian defence.
Both Carlsen and Anand inched to one point out of a possible two in the 10-player round-robin tournament following a draw in the opener too.
The other game to end early was a damp squib between former world champion Veselin Topalov of Bulgaria and Teimour Radjabov of Azerbaijan while Levon Aronian came up with a fine effort to outclass Hikaru Nakamura of United States.
In the other two games Sergey Karjakin crashed through the defences of Jon Ludvig Hammer of Norway and, in a surprise, Peter Svidler of Russia was outdone by Wang Hao of China.
After the end of the second round, Karjakin emerged as sole leader with a perfect two points out of a possible two and he is now followed by Aronian a half point behind.
Anand, Svidler, Nakamura, Calrsen, Topalov and Wang Hao share the fourth spot on one point each while Radjabov is ninth with ahalf point in his kitty. With seven rounds still to come, Hammer is at the bottom of the tables, yet to open his account.
Anand went for the principled Sicilian defence against Carlsen. The Norwegian had beaten Anand in the Moscow variation last time out and he stuck to the same but Anand was much better prepared this time. While the position remained equal Carlsen still had that nagging advantage he wanted to encash and Anand had to be precise in the defence even though it was not too difficult.
A rook and knight endgame was reached early and thereafter all Anand had to do was to get rid of the pawns off the board. The game was drawn with Carlsen having an extra knight but no pawns on the board on move 59.
Aronian crushed Nakamura out of an exchange Slav that speaks volumes about the world No 3. The position was about level out of the opening but the Armenian obviously had more ideas.
Nakamura thought he was fine when giving white a queen side pawn majority but he was proven wrong in the endgame as Aronian made most of it. In the end, the American fought vainly after losing a rook for lmost nothing. As it happened, nothing came of it and he had to resign after 70 moves.
Wang Hao played the game of the day outwitting Svidler in his pet Grunfeld. The Chinese was in command early in the opening and did not falter even while reaching an advantageous end-game.
Hammer lost with white which is certain to dent his confidence. Karjakin did everything right after getting a better endgame and won in 54 moves. (PTI)
Results: Magnus Carlsen (Nor, 1) drew with V Anand (Ind, 1); Veselin Topalov (Bul, 1) drew with Teimour Radjabov (Aze, 0.5); Levon Aronian (Arm, 1.5) beat Hikaru Nakamura (Usa, 1); Jon Ludvig Hammer (Nor, 0) lost to Sergey Karjakin (Rus, 1); Wang Hao (Chn, 1) beat Peter Svidler (Rus, 1).