With today's first two games of rapid chess both draws, Norway's Carlsen won the first game of the second blitz tiebreak - when the time limits were tighter - and looked to be heading to the quarter-finals.

But Russia's Esipenko hit back in the sixth game of the match, sending it to a third tiebreak, where the players had just five minutes plus a three-second increment per move, for each move.

Blitz virtuoso Carlsen won both of those matches for a hard-fought 5-3 win.

Five other matches were in tiebreaks today, and Carlsen's next opponent - Etienne Bacrot from France - needed two to over Kacper Piorun of Poland.

His compatriot Maxime Vachier-Lagrave, the seventh seed, was not so fortunate and was knocked out by Russian Sergey Karjakin.

Iran's Amin Tabatabaei, Pole Jan-Krzysztof Duda - who eliminated fifth-seeded Russian Alexander Grischuk - and the host nation's Vladimir Fedoseev all reached the last eight as well.

The Women's World Cup is being run in parallel in Sochi and only one quarter-final ran over to today.

Ukraine's Anna Muzychuk twice beat Nana Dzagnidze of Georgia to complete the semi-final line-up.