كتب : Hatem Maher
The ES Setif guardian allowed Paul Green to cut ahead of him and head in the opener after 31 minutes.
Another howler gifted Ireland, who missed out on a World Cup spot after a controversial defeat by France, their second goal seven minutes after the break.
Chaouchi failed to handle a tame cross from the left and instead pushed it into the path of Tottenham Hotspur striker Robbie Keane, who lifted the ball above him and into the net.
He was replaced in the 68th minute, making way for 24-year-old keeper Rais M'Bohli.
Keane wrapped up the victory when he a converted a penalty with five minutes remaining after he was brought down inside the area.
Algeria will face the United Arab Emirates on June 5 before flying to South Africa to take part in their first World Cup since 1986.
They will open their campaign against Slovenia June 13. They will also play England and the United States in Group C.