Anand went down 0.5-2.5 to Kramnik late on Thursday.
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The former world champion, who had lost in the first two rounds to Peter Svidler and Magnus Carlsen respectively, could not turn things around.
Anand lost the opening game despite some brilliant play as his Russian opponent fought back strongly.
A defeat in the second put the Indian No.1 on the back-foot and a draw in the third ended his hopes.
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World No.1 Carlsen shares the top spot with Svidler, with three victories and nine match points.
Meanwhile, world No.3 Ding Liren continued to struggle as he lost after leading 1.5-0.5 to Ukraine veteran Vasyl Ivanchuk.
Anand and Liren lie at the bottom of the table, without a win against their name.
The Indian meets Anish Giri (the Netherlands) in the fourth round later tonight.
All the round-robin games are best-of-four game contests.
Legends of Chess is an event where Carlsen, Liren, Nepomniachtchi and Giri, semifinalists at the Chessable Masters (part of the Magnus Carlsen Tour), received an automatic invite.
They are up against six legends aged 40-52, who have been at the top of world chess at various points in their career.
The tournament is part of the Magnus Carlsen Chess Tour. The winner of this event will qualify for the $300,000 Grand Final scheduled from August 9 to 20.
Results: Round 3: Vladimir Kramnik beat Viswanathan Anand 2.5-1.5; Vasyl Ivanchuk beat Ding Liren 2.5-1.5; Ian Nepominiachtchi beat Anish Giri 2.5-1.5; Magnus Carlsen beat Peter Leko 2.5-1.5; Peter Svidler beat Boris Gelfand 2.5-1.5.