The triumph over Grischuk came in the rapid game and this was the third mini-match that Anand won following his victory over Boris Gelfand of Israel in the third round.
It may be recalled that Anand had beaten Veselin Topalov in the opener and had then played out two draws with Vladimir Kramnik in the second round.
Levon Aronian of Armenia and Magnus Carlsen of Norway, however, remained at the helm following fine performances.
While Carlsen accounted for young Anish Giri of Holland 1.5-0.5, Aronian defeated Vassily Ivanchuk of Ukraine by a similar margin to remain on the leaderboard in the combined standings.
With seven rounds or 14 games still remaining, both Aronian and Carlsen have six points apiece and Anand is half a point behind.
In the blindfold standings, Aronian and Grischuk share the lead on three points each while Anand is tied third along with Carlsen and Azerbaijani Vugar Gashimov.
Carlsen leads solely in the rapid section with 3.5 points from four games and is closely pursued by Anand, Aronian and Topalov half a point adrift.
The blindfold game between Grischuk and Anand was the first one to finish after a mere 20 moves when a move repetition forced a draw. The World Champion went for the Berlin Defence of the Ruy Lopez and once again proved its solidity.
The idea he had prepared came on move 15, which apparently didn't catch Grischuk by surprise as he quickly played his move. The point of Anand's idea soon convinced White that he could not claim any advantage and should agree to a draw.
The rapid game ended in a win for the world champion but he was the first to admit that in the opening and middle game, his opponent had played better.
But once Anand realised that he had to defend and look for counter-chances cautiously, he used his chances better than Grischuk.
Anand could have decided the game quicker on the 38th turn, but when Grischuk failed to find the saving manoeuvre, he lost a piece and resigned two moves later.
Carlsen arrived seven minutes late for his blindfold game against Anish Giri. The Norwegian was under the impression that the second session started at a quarter past four and was chatting with a friend from his room.
Carlsen drew this game and then won the rapid game as black to continue with his winning spree.
The Amber tradition is coming to an end after this final edition. For the past two decades this has been a unique event with one blindfold and one rapid game in each round.
The blindfold games are played using a computer screen which has a blank chess board and only the last played move is shown.
In rapid, the players play a normal game. The total prize fund is 2,27,000 Euros (Approximately Rs 1.43 Crore).
Results round 4 Blindfold: Sergey Karjakin (Ukr) beat Vladimir Kramnik (Rus); Boris Gelfand (Isr) drew with Veselin Topalov (Bul); Alexander Grischuk (Rus) drew with V Anand (Ind); Magnus Carlsen (Nor) drew with Anish Giri (Ned); Hikaru Nakamura (Usa) drew with Vugar Gashimov (Aze); Levon Aronian (Arm) drew with Vassily Ivanchuk (Ukr);
Rapid: Kramnik drew with Karjakin; Topalov beat Gelfand; Anand beat Grischuk; Giri lost to Carlsen; Gashimov lost to Nakamura; Ivanchuk lost to Aronian.
Combined standings after fourth round: 1-2: Aronian, Carlsen 6 each; 3. Anand 5.5; 4. Grischuk 4.5; 5-8: Gashimov, Karjakin, Nakamura, Topalov 4 each; 9. Gelfand 3.5; 10.
Kramnik 2.5; 11-12: Giri, Ivanchuk 2 each.