They now have high hopes of getting past the group stage in Brazil, having set themselves the ambitious target of a place in the knockout round at the fourth attempt.
Drawn with Belgium, Russia and South Korea, their prospects might seem slim but are markedly better than four years ago when they failed to score a goal in South Africa and finished bottom of their group.
Civil and political turmoil coupled with years of poor returns for the Algerian national side had left the Arabic-speaking country a pale shadow of the team that had been among the early standard-bearers for the African game and had beaten West Germany at the 1982 World Cup.
They fell victim to one of the darker passages of play in World Cup history. Because of the way the group results had fallen, Austria and West Germany met in the last match knowing exactly what they had to do for both German-speaking neighbours to advance at Algeria’s expense.
In the event a fiasco of a match ended in a 1-0 win to West Germany meaning they both went through and Algeria went home.
Their surprise progress to the 2010 finals, after upsetting heavily fancied Egypt in a qualifying play-off, marked a dramatic change of fortune on which they have succeeded in building a more settled and confident team.
Algeria have constructed their side around a swathe of French-born players, drawn from the massive migrant population in Europe. Many of them switched allegiance after playing for France at junior level.
While Zinedine Zidane and Karim Benzema slipped through their grasp, these days players with Algerian connections in top European leagues are actively courted in an attempt to strengthen the squad.
Among the new recruits is 19-year-old Tottenham Hotspur midfielder Nabil Bentaleb, who won his first cap in March in a friendly with Slovenia, having represented France once at under-19 level.
The squad is under the control of an experienced coach who played in the 1982 World Cup finals for Yugoslavia, the 61-year-old Vahid Halilhodzic.
The Franco-Bosnian has an impressive coaching CV with experience in seven countries including Algeria and was unfortunate not to have taken Ivory Coast to the finals in 2010 when he was sacked after getting them there.
He is under no illusions about Algeria’s chances, but has said a place beyond the first round for the first time is a realistic target.
(Writing by Mark Gleeson in Cape Town; Editing by Josh Reich and Mike Collett)