Fred netted from close range in the 90th minute after good work by Marcelo and Hulk for his fourth goal in as many appearances for the national team.
Viktor Fayzulin had given Fabio Capello's side the lead after 73 minutes in front of 35,000 fans at the home of Chelsea.
Russia had a shout for a penalty early on when Vasily Berezutskiy's shot appeared to hit the arm of Fernando Lucas inside the box, but referee Howard Webb was unmoved.
Capello's men continued to dominate from set-pieces and only a last-ditch slide from Hernanes stopped Alexander Kerzhakov's goal-bound effort at the back post.
Neymar, who had been on the periphery of the match, burst through onto a through ball but could only shoot wide of Vladimir Gabulov's right-hand post.
Russia had gone off the boil after their blistering start to the game but Fayzulin injected some much-needed pace with half-time approaching. The Zenit winger skipped over the challenge of Lucas before releasing Kerzhakov down the left flank, Fayzulin ran on to collect the ball just inside the area but Julio Cesar tipped his resulting effort behind, although Webb incorrectly awarded a goal-kick.
The second half started at a much slower pace than the first and it was Brazil who shaded the possession without truly testing Gabulov, with Marcelo's 64th-minute shot comfortably held by the Anzhi goalkeeper.
Luiz Felipe Scolari, returning to Chelsea for the first time since his sacking in 2009, introduced Zenit striker Hulk with just over 20 minutes remaining with Blues midfielder Oscar making way.
Fayzulin's goal came seconds later after a melee inside the Brazilian penalty area. A number of players dallying in possession, as well as a clearance off the line from Hernanes, meant that Brazil looked like surviving the most threatening Russian attack of the second half. But Hernanes could only find Fayzulin with his clearance and the winger coolly converted from 12 yards out.
Brazil almost hit back immediately but Marcelo saw his powerful strike flash past the post with Lucas only picking out Gabulov with a long-range effort moments later.
Former Chelsea full-back Yuri Zhirkov did not have a happy return to his old ground as the 29-year-old was forced off with a hamstring problem late on after being introduced by former England boss Capello at half-time.
After Hernanes fired high and wide from an impossible angle, the equalising goal came on Brazil's next attack with Fred tapping home after Marcelo's ball across the face of goal.
Neither side could find a dramatic late winner as Capello and Scolari had to settle for a draw on their respective returns to London.