The ‘Desert Foxes’ set a pattern of away wins with South Africa defeating Congo Brazzaville 2-0 in Pointe-Noire, Mali beating Ethiopia 2-0 in Addis Ababa and Togo defeating Uganda 1-0 in Kampala.
Sierra Leone exceeded expectations by drawing 0-0 with Cameroon in Yaounde and Mozambique overcame Cape Verde Islands 2-0 in Maputo in other matches.
The matchday 3 qualifiers took place amid a demand from 2015 hosts Morocco that the January 17-February 8 tournament be postponed over the Ebola epidemic.
But the African Football Confederation (CAF) reacted Saturday by saying the three-week championship will go ahead as scheduled.
More than 4,000 people had died from the virus this year, according to the World Health Organisation, with virtually all the victims living in west African countries Guinea, Liberia and Sierra Leone.
Defenders scored both Algerian goals with Rafik Halliche putting them ahead on 10 minutes and substitute Djamel Mesbah adding a second in stoppage time.
Halliche nodded a corner past goalkeeper McDonald Harawa and Mesbah scored with a deflected close-range shot for the top-ranked team in Africa.
Victory before a capacity 30,000 crowd at Kamuzu Stadium lifted Group B leaders Algeria to nine points from three matches after defeating Ethiopia and Mali last month.
Another win over Malawi in Blida Wednesday would guarantee the 1990 African champions a top-two finish and a place among the 16 finalists.
Algeria did best of the five African qualifiers for the 2014 World Cup in Brazil, taking eventual champions Germany to extra time before suffering a 2-1 loss.
Malawi attacked for much of the second half and came closest to equalising when captain and midfielder Joseph Kamwendo struck a post.
South Africa made it three wins from five visits to Atlantic city Pointe-Noire by netting twice within four minutes soon after half-time.
Bongani Ndulula silenced a 15,000 crowd crammed into the Stade Municipal by scoring off a bicycle kick on 52 minutes.
Tokelo Rantie doubled the lead with a close-range shot after a superb pass from fellow England-based professional Dean Furman.
South Africa captain Senzo Meyiwa then made a string of saves to keep Congo at bay and when the Red Devils did score during stoppage time, the effort was ruled offside.
Success for Bafana Bafana (The Boys), who gave a debut to young defender Rivaldo Coetzee, lifted them to the top of Group A with seven points, one more than Congo.