On what turned out to be another fine day for Narayanan, he outplayed Kovalev after a long game with white pieces and took his tally to 4.5 points out of a possible five.
With eight rounds still to come, Narayanan now shares the lead with Jorge Cori of Peru and Lu Shanglei of China while there is a pack of seven players following them half a point behind and in tied fourth place.
Narayanan has been displaying top form and the fifth round was no exception.
The Budapest opening doesn't find many takers in GM level chess anymore but two important games involving Indians witnessed this. Kovalev went for it with black pieces and fell in a worse endgame even though Narayanan had to find most of his moves over the board.
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Leading to a rook and opposite colours endgame, Narayanan picked a couple of pawns and had no problems in converting those in to a full point.
Though, Grover's task was much harder, he still made it after 79 moves.
On a day when highest rated Indian Vidit Gujrathi was held to a draw by compatriot N Srinath, the other Indian GM Ankit Rajpara also could not break the ice and had to split points with Niranjan Navalgund. Both Gujrathi and Rajpara took their respective tally to 3.5 points apiece.
In the girls' championship being organised simultaneously, Padmini Rout played out an easy draw with black against Iran's Sarasadat Khademalsharieh to stay in joint lead after the second board between other overnight leaders Ann Chumpitaz of Peru and Daria Pustovoitova of Russia also ended in a truce.