He is within half a point of the leader and defending champion Sergei Zhigalko (5.5 points). Behind Zhigalko there are three players including Negi at five.
Negi, the Asian champion, who is still unbeaten, has drawn his last three games, but won the seventh round against Georgian Sanikidze (2586) to keep his title hopes alive.
He now has five points with three wins and four draws and Zhigalko (2667), who beat Anton Korobov (2705) has 5.5 points.
"Today was a wild game. I surprised him with an interesting novelty, and he took almost an hour to deal with it," Negi said.
"Eventually the time difference turned out to be the key, even though I missed chances to finish the game cleanly. But under increasing time pressure he failed to find the correct defenses in a wild game. It was nice to win after three draws."
The eighth round could see a pairing between Negi and Zhigalko and that may well give the Indian a chance to move ahead.
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Joining Negi at five points was Rauf Mamedov, who beat overnight joint leader, Baris Esen, while Mikheil Mchedlishivli also joined them at five beating Gulnar Mammadova.
The nine-round Swiss tournament is being held near the famous Aqua Park near Caspian Sea and carries a purse of USD 50,000 with the winner taking home USD 10,000.