Against all odds, the Flames top Group A with three points, following Sunday's draw between hosts Angola and Mali.
Two first-half goals from Russell Mwafulirwa and Elvis Kafoteka paved way for the famous win, before Dave Banda made it three after the interval.
Algeria boss Rabah Saadane had to start with Faouzi Chaouchi in goal, deputizing for the injured Lounes Gaouaoui.
Stunning Double
In the space of 45 minutes, the Flames managed to equal their overall goalscoring record in the history of the competition prior to the game.
It took them 17 minutes to beat Chaouchi, whose poor clearance into the body of Essau Kanyenda allowed Mwafulirwa to hit an empty net.
Surprisingly, Malawi didn’t look like holding back and the Algerians failed to make any response to their unlikely trailing.
In the 36th minute, defender Kafoteka doubled the Malawians lead with a superb header, following a pinpoint cross from Moses Chuvala.
Banda Killer
The second half started with no changes being made from the Algerian side and matters went from bad to worse for the Fennecs.
Three minutes after the break, Malawi struck again when Banda volleyed in on the rebound, following Mwafulirwa's effort against the post.
Once again the Algerians' response to the humiliation was anything but effective and Saadane waited until the 62nd minute to make his first substitution.
ES Setif hitman Abdelmalek Ziaya replaced veteran Rafik Saifi and the former missed an easy header from close range shortly after coming in.
Malawi boss Kinnah Phiri introduced the team's top scorer Chiukepo Msowoya, who missed a sitter from point-blank range to increase the deficit.
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