The Koreans dominated the early stages and broke the deadlock after six minutes when towering striker Kim Shin-wook reacted sharply to score from close range, capitalising on a weak header by Tarasov following a corner.
But Russia, who have now scored in all of their last 16 matches, levelled the score five minutes later thanks to a howler from Korean keeper Jung Sung-ryong.
The 28-year-old keeper failed to parry a simple-looking cross by captain Roman Shirokov and Fyodor Smolov was in the right place at the right time to complete the easiest of finishes with his second international goal.
The Koreans, who beat Switzerland 2-1 in a friendly in Seoul on Friday, almost restored their lead but Lodygin made a couple of brilliant saves to deny Lee Keun-ho and Ki Sung-yong.
Russia went ahead against the run of play 14 minutes after the break when Tarasov rose above the Korean defence to head in from Alexander Samedov's corner.
Lee Chung-young missed another golden scoring chance at the other end a few minutes from time.
A one minute silence was observed before the match in memory of the victims of the air crash in the Russian city of Kazan on Sunday, with Capello's men also wearing mourning ribbons.
Russia qualified for next June's World Cup finals after topping European Group F ahead of Portugal.
South Korea, ranked 56th in the world, will also play at the global showpiece in Brazil following an uninspiring qualifying campaign that saw them grab an automatic berth by the skin of their teeth.
(Writing by Angel Krasimirov, editing by Mark Meadows)
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