The scores are now level 1-1 in the 12-game title match, Topalov having taken the lead on Saturday after wininng the opening game.
Anand thus goes into the first rest day on Monday with a psychological advantage and the satisfaction of having played a marvelous game.
"I am happy with my play and I thought that I played fairly accurately," said Anand after the game.
The Indian ace started with the Queen pawn opening, a Catalan opening, which was a bit complex and difficult for the general chess enthusiasts to follow. The commenting Grandmasters were also divided in their opinion on which player had advantage in the opening.
After the rapid flurry of moves on Saturday in the opening stages, both players were on the slower side in Game 2. Topalov looked better in the opening stages but Anand played a patient game.
Anand had sacrificed a pawn in the opening and Topalov's pieces appeared to have greater mobility. The early exchange of queens on the 15th move was a bit surprising since it was at Anand's invitation and he was a pawn down.
Anand made a few unexpected moves and slowly seemed to be improving his position.
Topalov's 25th move to get into Anand's territory to exchange a knight for a bishop was dubious and the Indian started looking better. Anand spent too much time on the 29th turn and had just 19 minutes to Topalov's 38 minutes to complete the stipulated 40 moves before the first time control.
Topalov's 29th move was either unnecessary aggression or desperation in trying to exchange at least one rook as Anand's position had started looking better and better.
TheNIIT MindChampion first won a pawn and then the second one with his rooks, bishop and knight in perfect control even as Topalov's pieces were left with no play and he resigned on the 38th move.
Viswanathan Anand vs Veselin Topalov
1.d4 Nf6 2.c4 e6 3.Nf3 d5 4.g3 dxc4 5.Bg2 a6 6.Ne5 c5 7.Na3 cxd4 8.Naxc4 Bc5 9.00 00 10.Bd2 Nd5 11.Rc1 Nd7 12.Nd3 Ba7 13.Ba5 Qe7 14.Qb3 Rb8 15.Qa3 Qxa3 16.bxa3 N7f6 17.Nce5 Re8 18.Rc2 b6 19.Bd2 Bb7 20.Rfc1 Rbd8 21.f4 Bb8 22.a4 a5 23.Nc6 Bxc6 24.Rxc6 h5 25.R1c4 Ne3 26.Bxe3 dxe3 27.Bf3 g6 28.Rxb6 Ba7 29.Rb3 Rd4 30.Rc7 Bb8 31.Rc5 Bd6 32.Rxa5 Rc8 33.Kg2 Rc2 34.a3 Ra2 35.Nb4 Bxb4 36.axb4 Nd5 37.b5 Rdxa4 38.Rxa4 1-0