Fabio Capello's side had to come from behind to secure the win in Dubai, after Kim Shin-Wook poked South Korea ahead in just the sixth minute.
Fyodor Smolov drew Russia level shortly after, though, before Tarasov nodded home completely unmarked on 59 minutes to extend their unbeaten run to six games.
Capello made five changes from the 1-1 draw with Serbia last Friday, including Yuri Lodigin replacing Igor Akinfeev in goal and goalscorer Smolov coming in for Aleksey Ionov up front.
The Italian's opposite number, Hong Myung-Bo, meanwhile, also opted to make five alterations to the South Korea side after their 2-1 win over Switzerland, with Shin Kwang-Hoon, Lee Keun-Ho and Park Joo-Ho among those drafted in.
And Hong's side got off to the perfect start at the Zabeel Stadium when Kim bundled the ball past Lodigin from a corner.
However, their lead lasted just six minutes as some slick interplay between Roman Shirokov and Smolov resulted in the Dinamo Moscow man levelling matters.
South Korea responded well and had a number of good chances to regain their advantage before the break, but were let down by their final ball.
The Asian nation also started the second half on top, but were made to pay for a momentary lapse in concentration by Lokomotiv Moscow midfielder Tarasov.
The 26-year-old, winning just his second international cap, ghosted in to head past Jung Sung-Ryong just before the hour mark.
Confusion between Lodigin and his defence almost gifted South Korea a route back into the match in the closing stages, but Russia held on to make it four wins from their last six games in their final fixture of the year.
