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Playing against long-time rival after six straight losses, Anand won his first game of the tournament despite conceding early advantage on Monday night.
The Indian ace won in 45 moves with black pieces and continued the good work by claiming the second game in 49 moves.
Anand then settled for a 46-move draw in the third game against his 2012 world championship challenger.
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The victory moved the former world champion to the eighth spot with six points ahead of Hungarian Peter Leko (5 points) and Chinese world number three Ding Liren (3).
Anand, ranked 15th in the world, faces Liren in the eighth round later.
World number one Magnus Carlsen extended his lead at the top by defeating Peter Svidler 2.5-1.5 to reach 20 points while Russian Ian Nepomniachtchi needed an Armageddon to overcome Leko 3-2 and is close on the heels of the Norwegian with 18.
Legends of Chess is a unique event where Carlsen, Liren, Nepomniachtchi and Anish Giri, semifinalists at the Chessable Masters (part of the Magnus Carlsen Tour), received an automatic invite and are up against six legends aged 40-52, who have been at the top of world chess at various points in their career.
The winner of the event will qualify for the USD 300,000 Grand Final scheduled from August 9 to 20.
Results of Round 7: Viswanathan Anand (India) beat Boris Gelfand (Israel) 2.5-0.5; Ian Nepomniachtchi (Russia) beat Peter Leko (Hungary) 3-2; Magnus Carlsen (Norway) beat Peter Svidler (Russia) 2.5-1.5: Anish Giri (the Netherlands) beat Ding Liren (China) 2.5-1.5; Vasyl Ivanchuk (Ukraine) beat Vladmir Kramnik (Russia) 3-1.