The Desert Warriors attacked from the kick off and should have had a penalty inside 10 minutes when Sofiane Feghouli was felled in the area.
But they didn't have too long to wait to celebrate as Slimani rampaged onto Carl Medjani's ball over the top, held off two defenders and clipped a neat finish beyond Jung Sung-ryong.
It was a moment of pure ecstasy for the Algerians and just two minutes later they were propelled into dreamland as Fulham reject Rafik Halliche rose highest to thump home a header from a left-wing corner.
The South Koreans had no answer to the vibrant play of Vahid Halilhodzic's side and it was three just seven minutes before the break when Slimani made the most of a long ball and coolly rolled it to Abdelmoumen Djabou to steer past the keeper.
The Taeguk Warriors responded after the break and pulled one back through Son-Heung Min's superb turn and shot before Yacine Brahimi restored the three-goal advantage with a low finish after exchanging a wonderful one-two.
South Korea kept going and Koo Ja-cheol diverted home with 18 minutes left but Algeria held on to claim their first World Cup win since 1982 and become the first ever African side to score four goals in a finals match.
PRE-MATCH: All change, no change. South Korea stick with the same XI that started the draw with Russia. Algeria make FIVE changes as they bid to keep their last 16 hopes alive.
4' - PENALTY SHOUT. Kim appears to trip Feghouli in the area and when the ball drops for Brahimi, the forward skies a volley over the top. Was that a penalty? Certainly could have been given.
9' - ALGERIA CHANCE! South Korea are all at sea in defence and a left-wing cross finds Slimani unmarked at the back post but he nods his free header into the side netting.
26 - GOAL! ALGERIA 1-0 SOUTH KOREA. Slimani rampages onto Medjani's ball over the top and dinks a cute finish over Jung Sung-ryong after holding off two challenges.
28' - GOAL! ALGERIA 2-0 SOUTH KOREA. A corner from the left is met by the towering leap of Halliche who scores with a bullet header – the Fulham reject has become a World Cup hero.
38' - GOAL! ALGERIA 3-0 SOUTH KOREA. Korea can't deal with a long ball by Medjani. It falls to Slimani who just rolls it across to Djabou to finish with aplomb.
50' - GOAL! ALGERIA 3-1 SOUTH KOREA. South Korea have one back. Another long ball catches the Algerian defence napping this time and Son Heung-min pivots brilliantly before hitting a low shot under the keeper. Game on?
60' - WHAT A SAVE! Ki Sung-yueng lets fly with an audacious drive from distance that looks to be searing into the top corner, but M'Bolhi dives full stretch to get fingers to it and tip it away.
63' - GOAL! ALGERIA 4-1 SOUTH KOREA. Algeria burst forward and restore the three-goal lead. It's a sweet move as Brahimi exchanges a brilliant one-two and slides the ball under the keeper.
72' - GOAL! ALGERIA 4-2 SOUTH KOREA. Koo Ja-cheol is on hand to divert the ball into the net from inside the six-yard box from Lee Keun-ho's cut back. Now, can they make this interesting?
88' - SOUTH KOREA CHANCE! Ji Dong-won races onto a knock down but drags wide from 18 yards. Time running out for Korea.
Algeria ended a run of seven World Cup matches without a win.
Algeria scored more goals in this match than they did in their preceding seven World Cup matches combined.
There were more goals in this game than in Algeria's previous four World Cup matches combined (5).
Algeria scored with four of their 15 shots on goal (including blocked shots); they managed three shots in total against Belgium (inc. blocked).
20 of the 23 shots in this game came from inside the penalty area.
South Korea have won one of their last seven World Cup group games.
Rafik Halliche completed 31 first-half passes in this match, more than any Algeria player managed in total against Belgium.
24 of South Korea’s 31 World Cup goals have come after half-time (including one extra-time goal).
The last eight World Cup goals conceded by Algeria have come after half-time.
Algeria became the first African team to score four or more goals in a World Cup match.
South Korea have conceded 11 goals in their last four World Cup matches – they conceded six in their preceding eight.
Of teams playing in this tournament, only Germany’s games in all World Cups have produced a higher average number of goals than South Korea’s 3.23.
MATCHCAST: FULL COMMENTARY AND STATS TALKING POINT
This World Cup continues to deliver! On paper this game looked like one of the less attractive encounters of the competition with a goal-shy Algerian side taking on a South Korea who needed a goalkeeping howler to score against Russia. A drab draw would be a solid bet - but not at this World Cup. A six-goal thriller and more momentous milestones means Algeria are on the brink of a dream spot in the last 16.
MAN OF THE MATCH
Yacine Brahimi (Algeria) - A constant menace in attack with South Korea failing to deal with his clever dribbling throughout. Capped his display with a well-worked goal and fully justified his inclusion.
ALGERIA - Mbolhi 6, Bouguerra 7, Halliche 7, Mesbah 7, Feghouli 8, Brahimi 8, Medjani 6, Slimani 8, Bentaleb 6, Djabou 6, Mandi 6. Subs: Ghilas 6, Lacen 6, Belkalem n/a.
SOUTH KOREA - Jung Sung-ryong 5, Kim Young-gwon 5, Lee Yong 5, Yun Suk-young 5, Hong Jeong-ho 6, Lee Chung-yong 6, Han Kook-young 5, Park Chu-young 5, Koo Ja-cheol 6, Ki Sung-yueng 6, Son Heung-min 7. Subs: Kim Shin-wook 6, Lee Keun-ho 6, Ji Dong-won 6.
THE MATCH IN A TWEET
- Sports & Recreation
- South Korea
- Carl Medjani