Anand, who first made it to the World's top-10 in July 1991, has remained India's top-ranked player in all published lists since January 1987.
Teenaged Grandmaster D Gukesh posted a win over home favourite Misratdin Iskandarov in a second round match of the World Cup in Baku, Azerbaijan, on Tuesday and overtook his idol Viswanathan Anand in live world (FIDE) rankings.
The 17-year old Gukesh outclassed Iskandarov of Azerbaijan in 44 moves in the second game of their second-round match.
"Gukesh D won again today and has overcome Viswanathan Anand in live rating! There is still almost a month till next official FIDE rating list on September 1, but it's highly likely that 17-year-old will be making it to top 10 in the world as the highest-rated Indian player," the international chess federation (FIDE) said in a tweet.
The latest gain of 2.5 rating points took Gukesh's live rating to 2755.9, while Anand's is 2754.0. As a result, Gukesh replaced Anand as the World No. 9 in live rankings while the five-time World champion slipped to 10th.
Anand, who first made it to the World's top-10 in July 1991, has remained India's top-ranked player in all published lists since January 1987.
Gukesh will take on compatriot S L Narayanan in the third round.
Meanwhile, a bunch of Indians advanced to the third round on Thursday. In the men's section, GM R Praggnanandhaa, a winner over Maxime Lagarde, Nihal Sarin won while D Harika and R Vaishali moved into the next round.
Indian GM B Adhiban bowed out, losing 0.5-1.5 to Daniil Dubov while unfancied compatriot Karthik Venkataraman held the No.2 seed Hikaru Nakamura to a 1-1 score and forced a tie-break.
Asian Champions Trophy: India maul China 7-2; Pak lose
PHOTOS: West Indies vs India, 1st T20I
Eng's Bazball against India will fascinating: Hussain
South Zone lift Deodhar Trophy for 9th time
Hussain backs Anderson to hit form against India