The African nation raced into a three-goal in the first half and, though they were made to work in the second period, sealed a crucial victory
Vahid Halilhodzic's men ran riot in the opening 45 minutes as the South Korea defence was found wanting time and again.
Islam Slimani opened the scoring midway through the opening period by lifting the ball over goalkeeper Jung Sung-ryong from a long-range pass, before Rafik Halliche doubled the advantage and Abdelmoumene Djabou made it three.
Son Heung-min stopped the rot by slotting the ball between the legs of Rais M'Bolhi to reduce the deficit just after the interval, but it proved to be brief respite for the 2002 World Cup co-hosts.
Yacine Brahimi appeared to put the result beyond doubt in the 62nd minute, but a Koo Ja-cheol strike 10 minutes later kept the match alive as a contest.
However, Korea were unable to set up a nervy end to the game as Algeria went two points clear of Russia in second place in Group H with one game left to play.
Algeria - a team who failed to score a single goal in South Africa in 2010 - become the first African nation to score four goals in a World Cup fixture.
While South Korea were unchanged from their 1-1 opening draw with Russia, Halilhodzic made five changes to the Algeria side that started the 2-1 defeat to Belgium.
Sofiane Feghouli, who scored from the spot in Algeria's curtain-raiser, blasted over on the turn in the opening two minutes before Brahimi joined him in clearing the crossbar following a goalmouth scramble moments later.
Algeria had appeals for a penalty turned down in the build-up to Brahimi's effort, after Feghouli appeared to be felled by Kim Young-gwon, but the men from north Africa continued to look the more threatening.
Slimani – one of those brought into the starting XI - headed narrowly wide of the left-hand post from a corner 10 minutes in, and the Sporting forward should have done better when he failed to direct the ball goalwards from a delightful Aissa Mandi cross.
But the 26-year-old justified his selection in the 26th minute when he latched onto a Carl Medjani punt from the back to clip the ball over Jung, who was in no man's land as Algeria doubled their advantage less than two minutes later.
Halliche was given too much space by the Korean defence and rose highest to power home a thunderous header from a Djabou corner and punish the flapping Jung.
South Korea's vulnerable backline was exposed once more, seven minutes before the break, as Djabou had the time to slot into the bottom right-hand corner as puzzled defenders stared at each other blankly.
Half-time will have been welcomed by the Asian nation, for whom the match was turning into a horror show, but Hong Myung-bo's men emerged for the second 45 minutes with renewed energy.
And they pulled one back in the 50th minute. Son controlled the ball somewhat fortuitously in the penalty area after it bounced off his back before firing between the legs of Algeria keeper M'Bolhi, who then had to be alert to tip over a long-range effort from Ki Sung-yueng.
Brahimi exchanged passes brilliantly with Slimani and buried Algeria's historic fourth just after the hour mark, but captain Koo bundled home from a Lee Keun-ho cross to keep South Korea's hopes alive.
The two-goal advantage was untroubled for the remainder of the encounter,though, as Algeria clung on for their first World Cup win since 1982.