Islam Slimani, Rafick Halliche, Abdelmoumene Djabou and Yacine Brahimi were the heroes for the African side and gave them every chance of reaching the knockout stages of the competition.
South Korea, who reached the semi-finals of the World Cup back in 2002, now have to win their final group game if they are stand any chance of making the last 16.
Algeria stunned their opponents when they raced into a three goal-lead and got off to the perfect start when they broke the deadlock on 26 minutes.
South Korea failed to deal with a long ball played over the top of the defence and Slimani fired the ball home.
Algeria doubled their lead just two minutes later following more poor defending as Djabou’s corner picked out Halliche who directed a powerful header into the back of the net.
Djabou put the game beyond South Korea when he added a third on 38 minutes when he struck home from 10-yards.
South Korea refused to lie down and pulled a goal back on 50 minutes when Son Heung-min struck the ball through the legs of the Algeria keeper.
But Algeria ensured there was no comeback and made it four on 62 minutes when Brahimi fired home from close-range.
The drama continued as Koo Ja-cheol pulled a second back for South Korea on 72 minutes but it not enough to stop Algeria coming away with a memorable victory.
Divock Origi is congratulated by Kevin De Bruyne
Earlier Belgium secured their second win of the tournament, defeating Russia 1-0 in the Maracana.
The victory leaves Mark Wilmots's side assured of a place in the last 16 while Fabio Capello's Russia must defeat Algeria on Thursday to stand any chance of progressing.
The game's decisive goal came from Divock Origi, a 19-year-old of Kenyan parentage, who has played only 12 senior club matches.
