Victor Fayzulin put Russia ahead in the 73rd minute at London's Stamford Bridge, netting at the third attempt after the Brazil defence had cleared three shots off the line.
Brazil, who struggled to create chances despite enjoying plenty of possession, levelled when Marcelo got free on the left and his low cross was tapped in by Fred who scored for the third game running.
Five-times world champions Brazil have yet to win since Scolari was re-appointed, losing to England last month before drawing 2-2 with Italy last Thursday.
Russia, frustrated by the postponement of their World Cup qualifier against Northern Ireland because of heavy snow in Belfast on Friday, started brightly.
Fabio Capello's team, unbeaten in their previous seven games, had the better of the opening exchanges when only good goalkeeper by Julio Cesar and a timely interception from Hernandes stopped them from going ahead.
Brazil were quick to respond with Kaka and Oscar, playing at his club's home ground, at the heart of some promising counter-attacks.
However, Brazil did not particularly trouble goalkeeper Vladimir Gabulov and Russia came closest to breaking the deadlock when a swift counter-attack ended with Fayzulin firing into the side-netting after a quick breakaway.
Kaka, seeking to establish a permanent place in the side after an absence of nearly two years following the 2010 World Cup, did his chances no harm with an encouraging performance that included one superb passing exchange with Oscar and Neymar early in the second half.
Fayzulin put Russia ahead in the 73rd minute after Thiago Silva and Julio Cesar had blocked shots on the line.
Brazil appeared to be heading for a demoralising defeat until Hulk released Marcelo and his cross was fired in from closed range by Fred.
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