However, Malawi defied their status as rank outsiders by going 3-0 up inside 50 minutes.
"We know we are being treated as the underdogs," said Malawi midfielder Josephy Kamwendo.
"We are playing against big teams but, like them, we are here to win."
The Flames started positively and took the lead when Chaouchi attempted to clear a long ball, but only succeeded in smashing it straight into advancing striker Essau Kanyenda.
The ball broke to Mwafulirwa, who gratefully smashed it home.
Rafik Saifi should have levelled after 24 minutes when he was played in by Karim Ziani's ball behind the defence but he put his lobbed effort over the bar.
Malawi overcame their underdog billing to boss the Algerians for spells
Ten minutes before half time, Kafoteka made it 2-0 as he rose highest to head home Hellings Mwakasungula's pinpoint cross.
Just three minutes into the second half, Malawi made it a rout when Chaouchi flapped at a cross and after a scramble and an attempted clearance from Madjid Bougherra, the ball fell to Banda who stroked it in.
Algeria had a decent penalty shout denied later in the second half, but failed to offer much more in a disappointing performance.
"We didn't play well," Algeria coach Rabah Saadane said. "We still have a chance to progress but we need to play well against Mali."
The result puts the Flames top of Group A ahead of Angola and Mali, and leaves World Cup qualifiers Algeria, who will be in the same group as England in South Africa later this year, bottom.
The Desert Foxes were tipped by some as potential winners, having travelled to Angola full of confidence after beating African champions Egypt in a World Cup qualifying play-off in November.
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