Mr Putin lauded both players for "an outstanding game."
Viswanathan Anand beat Gelfand of Israel on Wednesday 2.5-1.5 in a rapid tiebreaker following a 6-6 draw played at the Tretyakov Gallery, one of Russia's finest museums.
Mr Gelfand, who was born in the Soviet Union and emigrated from Belarus to Israel in 1998, was cheered throughout the match as if he were a home player.
Mr Anand told Mr Putin over tea that he had learned to play chess in a Soviet cultural center in his hometown when he was a child.
"So we brought this on ourselves!" Mr Putin said.