Kosteniuk is competing for Switzerland after switching from the Russian National Federation this year.

The 2021 World Cup winner was stunned at the Baku Marriott Hotel Boulevard by Serbia's Teodora Injac in the women's tournament.

The pair had won one game each the day before and as a result were forced into a tiebreak.

Injac made no mistake this time as she defeated her opponent in both games of the first rapid tiebreak.

In the first, Kosteniuk missed an opportunity to take a perpetual check which allowed Injac to secure victory.

"I think I got a little bit lucky in the first game as the whole game I played on 30 seconds against her 10 minutes or so," said Injac. 

"That was very difficult to hold and luckily she blundered. 

"After that game it was really difficult for her to recover."

In the open tournament, one of the favourites Anish Giri of The Netherlands was also eliminated.

He lost to 28-year-old Nijat Abasov, who hails from the host city, following three tiebreak matches which lasted a combined five hours.

"Before the match, it was never 50/50," Abasov said after his win.

"Of course he was one of the favourites for the event and world number seven so he was clear favourite but with reduced time control my chances would be more.

"That's how it turned out."

It was not all success for the hosts as 2019 World Cup winner and the biggest Azerbaijan hope Teimour Rajabov was knocked out.

He suffered at the hands of Spanish Grandmaster Jaime Santos Latasa who was playing with black.

Santos Latasa took the first tiebreak after Rajabov badly misplayed in a rook and queen endgame before the second ended in a draw.

The United States' Fabiano Caruana defeated Turkey's Mustafa Yılmaz 2-0 to qualify for round four.

He was the only player of the men's favourites to finish the tiebreak with a 100 per cent record.