A breathtaking first-half performance contributed to a 4-2 Group H win over South Korea on Sunday, sending Algeria two points clear in second place with one game to go.
Coach Halilhodzic was pleased to have registered a first Algerian win at the finals since the 1982 tournament in Spain.
"I'm very happy," he beamed. "A victory after a 32-year wait in the World Cup, it's beautiful.
"I must thank the players for their efforts. We delivered an excellent first half before falling in the second half.
"The players lost a bit of concentration, but the most important thing is the victory."
Islam Slimani broke the deadlock in the 26th minute, before Rafik Halliche and Abdelmoumene Djabou made it 3-0 prior to half-time.
Son Heung-min pulled one back for Korea after the break, but Algeria's three-goal advantage was soon restored when Yacine Brahimi found the net in the 62nd minute.
Koo Ja-cheol reduced his side's deficit to two once again 10 minutes later, yet the Koreans had left themselves with too much to do as Algeria held on for a memorable triumph.
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