With his third draw in as many games, Anand inched himself up to 1.5 points out of a possible three and other results in the round helped the Indian jump to joint fourth spot in the rankings with six rounds still remaining in the strongest tournament of the year.
Hikaru Nakamura of United States punished Fabiano Caruana of Italy for some reckless play while Veselin Topalov's crushed Maxime Vachier-Lagrave of France in the two decisive games of the day.
Nakamura and Topalov emerged as the new joint leaders on 2.5 points each and Giri is on the heels of the leader a half point behind.
Anand, Caruana and Vachier-Lagrave share the fourth spot on 1.5 points apiece while Grischuk, Aronian and Hammer are right behind them with one point in their kitty. Magnus Carlsen continues to find himself in an unfamiliar last spot on a half point.
"I am one of the worst for recollecting my analysis," Grischuk said after the game.
For a brief moment in the middle game, Grischuk had some chances, but the Russian, running out of time on the clock, allowed a queen trade after which Anand was on top again. However Grischuk found the right defense and the game soon petered out to a draw.