Islam Slimani, Rafik Halliche, Abdelmoumene Djabou and Yacine Brahimi scored for Algeria, who had taken a 3-0 lead at halftime, reports Xinhua.
South Korea, who finished the first half without any shot, dashed out in a strong second half, but the effort it wasn't enough to turn the match around.
Algeria climbed to second place with the three points in Group H ranking behind Belgium on six points.
South Korea had kept an undefeated record against African teams in the previous World Cups, having beaten Togo 2-1 in 2006 and drawn 2-2 with Nigeria four years ago in South Africa.
However, the record came to an end after an extremely poor first half.
Algeria, who were facing an Asian team for the first time in the World Cup, planned a five-defender formation, but their attack was much more threatening than their opponents.
After a long spell of possession, 'Les Fennecs' caused trouble in the South Korean area in the fifth minute. Sofiane Feghouli was taken down in the box, but his teammate Yacine Brahimi's follow-up went above the bar.
South Korea started to counter attack after ten minutes, but Algeria still controlled the match.
The first goal came in the 26th minute, Slimani caught the long pass between two South Korean defenders. He dashed into the box and tipped the ball over Jung Sungryong.
The Algerians didn't have to wait too long for their second goal. Two minutes after the first goal, center back Rafik Halliche made use of a corner play, heading in the ball to give Algeria a 2-0 lead.
South Korea tried hard to fight back, but the counterattack of Algeria resulted in another goal.
In the 38th minute, Slimani caught another long pass, and sent the ball to Abdelmoumene Djabou, who was left completely free. Djabou seized the chance, netting the cross to make it 3-0 for Algeria.
South Korea opened the second half with a 50-minute goal. Striker Son Heungmin picked up a pass, broke through the defence and powered a shot through Adi M'Bolhi's legs to get back a goal for South Korea.
The Asian team had the momentum after the goal, making consecutive attacking efforts, and put the Algeria defence under pressure.
After repelling several high-quality shots from South Korea, Algeria finished another counter attack with a goal.
South Korea couldn't turn around the game after trailing 0-3 at half-time
In the 62nd minute, Brahimi and his teammates completed a break through the South Korean defence. Brahimi's easy shot went past Jung Sungryong, and Algeria extend the lead to 4-1, becoming the first African team to score four or more goals in one match.
South Korea refused to give up. Koo Jacheol made a strong finish after a string of passes and cut the gap to two goals again in the 72nd minute.
South Korea kept the pressing aggressively, but failed to score again.