The result left the teams in joint second place in Group H after the first round of matches behind leaders Belgium, who earlier came from behind to win 2-1 against Algeria in Belo Horizonte.
Kerzhakov, the sole surviving member of Russia's last World Cup team at the 2002 finals in Asia, scored in the 74th, three minutes after coming on, to notch his 26th international goal.
The 31-year-old swivelled and struck a shot from inside the six-yard box after fellow substitute Alan Dzagoev's effort was parried by goalkeeper Jung Sung-ryong.
"I'm happy but I'm sorry at the end because we could have won the game. There was a wonderful reaction by our team after the goal we suffered," Russia coach Fabio Capello said.
"We developed a crescendo, we grew (in a way) that was important for me," he told reporters.
The South Koreans had taken the lead six minutes earlier when an awful blunder by Akinfeev handed substitute Lee Keun-ho the opening goal at the Pantanal arena.
The 2012 Asian Footballer of the Year unleashed a stinging shot from outside the box that the seasoned Akinfeev appeared to have under control but let slip from his grasp and over his shoulder into the net.
Korea's coach Hong Myung-bo said he told Lee when he sent him on that the Russians "would be tired and slowing down and he should prepare for that and be more aggressive.
"I think our players really did their utmost on the pitch today. Tactically and physically each and every moment they played intelligently," Hong told reporters.
GOAL RELIEF
The match was lifted from its torpor by the goal after a chess-like first half of ebb and flow but little danger to the goalkeepers in which young South Korea striker Son Heung-min put two chances well over the bar.
In the 10th minute, Yoon Suk-young hit a long high ball down the left wing and Koo Ja-cheol headed it into the middle where Son took off on a fast diagonal run into the right side of the box where he shot too high.
The 21-year-old striker, a thorn in the Russian defence and voted man-of-the-match, had another chance in the 39th minute when he found space in the middle but his effort from the edge of the box again sailed high over the bar.
Capello said his players took time to get into the match.
"At the beginning, our players were so nervous, I don’t think they were as smooth as they normally are. After the goal we suffered, they reacted," he said.
Russia tried to stretch the Korean defence through Yury Zhirkov on the left wing and Alexander Samedov on the right.
Samedov found the angle too tight in the 20th minute and shot wide but on the half-hour when he was fouled 25 metres out by Ki Sung-yueng, who was booked, keeper Jung managed to beat away centre back Sergey Ignashevich's powerful free kick.
South Korea captain Koo had a shot deflected just wide of the post off the leg of his opposite number Vasili Berezutskiy for a corner in the closing minutes of the first half.
The goalkeepers were called more into action in the second period, Jung having to tip a Victor Faizulin shot over the bar almost from the restart.
At the other end, the experienced Akinfeev was equal to everything the Koreans threw at him, notably a bullet of a free kick from central defender Kim Young-gwon, but he fumbled the apparently easier shot he had to take from Lee.
Both sides, who at this stage look set to fight over second place, went all out for a win in the dying stages with Samedov ballooning a Russian chance high into the air after the ball had crossed the Korean box.
(Editing by Nigel Hunt and Ken Ferris)
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