Algeria led 3-0 at halftime, but withstood a stronger South Korean second half performance to claim its first World Cup win since 1982.
Slimani scored on 26 minutes and, two minutes after the restart, defender Rafik Halliche headed in a corner. Algeria made it 3-0 in the 38th when Abdelmoumene Djabou side-footed home.
South Korea started positively after the break and pulled a goal back on 48 minutes when Son Heung-min shot through the legs of Rais Mbolhi.
Yacini Brahimi then scored for Algeria before South Korean captain Koo Ja-cheol bundled home his teams second goal.
More Sports Headlines
Seahawks do what rest of salary-capped NFL say teams can't do Mariners beat Twins 4-3 in 11 innings Snohomish mixed martial artist returns to her first love AquaSox strand 10, fall 3-2 to Volcanoes Seahawks release DT McDaniel , acquire CB Seisay Benches empty as Royals fall to Blue Jays Rays demote Moore, place Souza on DL with fractured hand Charles scores 29 points, Liberty beat Storm 78-62
Our new comment system is not supported in IE 7. Please upgrade your browser here.