It was the North Africans' first World Cup victory since their famous 1982 success against West Germany and was the first time an African side had managed four goals in a single World Cup match.
First half goals from Islam Slimani, Rafik Halliche and Abdelmoume Djabou did the damage as Korea were on already their knees at the break.
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The result spirited Algeria up to second in Group H behind Belgium, with Russia and the Koreans trailing on one point apiece.
On a perfect afternoon in this southern port city, Algeria came out fighting for their World Cup lives, only too aware defeat would send them home.
Sofiane Feghouli and Slimani tested Korean keeper Jung Sung-Ryong in the opening minutes. Algeria's pleas for a penalty on five minutes in a chaotic goalmouth scramble were firmly rejected by Colombian referee Wilmar Roldan.
But their impressive start reaped its initial reward when Slimani raced onto Carl Medjani's lob, saw off Korean defenders Hong Jeong-Ho and Kim Young-Won and flicked the ball past Jung.
The rattled Koreans were picking the ball out of their net again two minutes later when Halliche out-jumped his markers to head in Djabou's corner from the left.
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