In yet another excellent tournament match, the Africans stormed into a 3-0 half-time lead following three goals in 12 minutes midway through the opening period.
Korea improved after the break, pulling a goal back. However, they conceded a killer fourth goal and Algeria held on for all three points.
Below, Sports Mole chews over the 90 minutes of action from Porto Alegre.
On target: 4
On target: 5
Was the result fair?
Following a simply brilliant first-half display, Algeria absolutely deserved all three points here this evening. They showed real ambition from the very first minute, having 10 shots before South Korea had even registered one. The Asians improved greatly after the break, probably deserving their two goals. But the game was won and lost before half time, and for that reason both teams got what their performances merited here.
South Korea performance
After an encouraging point against Russia, South Korea wanted to build on their chances of progression. Manager Hong Myung-Bo named an unchanged lineup, but their performance in the first 45 minutes was woeful. They were on the back foot from the off, with the defence struggling to contain Islam Slimani and Sofiane Feghouli.
Following the interval, they did improve, and once Kim Shin-Wook was introduced, their game plan became more obvious. With him winning the flick-ons, Son Heung-Min saw more of the ball. However, the killer blow was the fourth goal, and Hong's team were never coming back after that.
Though not quite the same swagger that France or Holland have shown in Brazil so far, Algeria were certainly better tonight than anything Belgium, Spain or England have served up. Their mixed range of long and short passing destroyed the South Koreans before the break, with Slimani, Feghouli and Yacine Brahimi starring.
Brahimi's goal - Algeria's fourth - was both crucial and brilliant. It came at a vital time, just as Korea felt they were getting back into the contest, but it killed them off and they were worthy of taking all three points. Their 32-year wait for a World Cup victory is deservedly over.
Sports Mole's man of the match
Islam Slimani: Brahimi and Feghouli might feel hard done by, though in truth any of three of them could be worthy winners of this award. Slimani was drafted into the team and was magnificent in the opening half, scoring the first and creating the third for his team.
He was unlucky not to score early on, so when he was able to lift the ball over Jong after 24 minutes the delight on his face was clear to see. His performance slightly tailed off as the game wore on, but he was so crucial before half time that he is a worthy man of the match.
This was a game of few errors, despite six goals. Perhaps the biggest gaffe came from the South Korean defensive pairing of Kim Young-Gwon and Hong Jeong-Ho, who were both taken out of play by one touch from Slimani. The forward pulled a pass out of the air but instead of one of the defenders going to intercept him, they both tried, allowing him to roll the ball into the path of Abdelmoumene Djabou to make it 3-0.
Colombian Wilmar Roldan waved away a late penalty appeal from Son, probably correctly. The forward was hit from behind but perhaps went down too softly. Aside from that, the only question marks over Roldan's performance were that he seemed reluctant to book anyone early on, despite some poor challenges going in. He rightly cautioned Algeria captain Madjid Bougherra for a bad tackle, also on Son.
South Korea: With Belgium needing a point to guarantee top spot in Group H, South Korea will have their work cut out to qualify for the round of 16. From what they've shown us so far, it would surprising to see them triumph and progress on Thursday.
Algeria: Now in second spot, Algeria have to be the favourites to go through with their fate now in their own hands. Russia will know that they can still qualify with a win against the Africans, but Vahid Halilhodzic's men won't fear a side who have looked out of sorts in their two games to date.