Zambia moved into second place in Group B as they advanced to four points, but are still five points behind leaders Nigeria, who won 4-0 at home to Cameroon on Friday.
Algeria are virtually out of the race after having qualified for the 2010 and 2014 finals, where they reached the round of 16. They have just a single point with three games to play.
Algeria's preparations were disrupted by a decision to allow African Footballer of the Year Riyad Mahrez to return to Europe to try and secure a transfer away from Leicester City, which proved unfruitful. As a result, he missed Saturday's game.
Mwila hit the upright in the fifth minute before finding the net within 60 seconds, rising between two Algerian defenders to head home a cross from Augustine Mulenga.
Teenage prodigy Patrick Daka set up a second goal in the 33rd minute as he cut in to cross for Fashion Sakala, whose scuffed shot was parried by Algeria goalkeeper Rais Mbolhi, with Mwila first to the rebound.
Algeria pulled a goal back with powerful left-footed shot from Yacine Brahimi in the 55th minute and were given a further window of opportunity when debutant Sakala, 20, was dismissed for a second cautionable foul a minute later.
But 19-year-old Enock Mwepu, also making his international debut, came on to score on the counter in the final minute to make sure of home success.
(Reporting by Mark Gleeson in Cape Town; Editing by Neil Robinson)
