Ireland took the lead just after the half hour when Derby County midfielder Paul Green, who made his international debut as a substitute in the 2-1 win over Paraguay, stooped low to head home winger Liam Lawrence's free kick unmarked.
They doubled it six minutes into the second half when visiting goalkeeper Faouzi Chaouchi flapped at a Damien Duff cross and captain Robbie Keane dinked the ball over Chaouchi and his watching defenders.
Algeria, who upset African champions Egypt en route to their first appearance at the finals since 1986, started with debutants Habib Belaid, Adlane Guedioura and Djamel Mesbah, and looked like a side that had not played much football together.
The trio, among seven uncapped players included in coach Rabah Saadane's preliminary squad for next month's finals in South Africa, made little impact in a side where only dangerman Karim Ziani mildly impressed.
The VfL Wolfsburg attacker gave Irish goalkeeper Kieren Westwood his only test of the evening shortly after Keane's goal, forcing him to push away a long range drive.
Guedioura would have marked his first appearance with a goal were it not for the crossbar but the Algerians were further behind within a minute when Keane tucked away an 86th minute penalty that he had won.
It could have been worse for the North Africans who have World Cup Group C matches against England, United States and Slovenia ahead but Keane was earlier denied first by a smart save by Chaouchi and then by the goalkeeper's post.
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