The Desert Foxes picked up their first World Cup victory in 32 years after a three-goal first-half blitz at Estadio Beira in Rio.
Man of the match Islam Slimani, defender Rafik Halliche and forward Abdelmoumene Djabou gave the North Africans a convincing lead as they overpowered the 2002 semi-finalists.
Son Heungmin pulled a goal back for South Korea at the beginning of the second half before Yacine Brahimi – who switched allegiance from his native France last year – restored Algeria’s advantage with a tidy finish after a one-two with Slimani on the edge of the area.
South Korea captain Koo Jacheol then pulled another back with 18 minutes remaining, but Algeria held on for the historic win.
Coach Vahid Halilhodzic, who guided Ivory Coast to the last World Cup but was fired before it started, knows his team can reach the second round for the first time by beating Russia on Thursday.
Russia can also progress with a win if South Korea fails to defeat Belgium.
If Algeria and Russia draw, South Korea can go through by beating Belgium.
If Russia and South Korea both win, the Asian side will have to do so by two more goals to overcome its differential deficit.
Algeria became the first African country score 4 goals in FIFA World Cup.The match ended 4-2 in favour of Algeria.