Saladin, who also scored in the 1-1 draw against South Africa last week, netted in the 38th minute and again two minutes before the end.
It was a deserved win for the Walias who dominated throughout but wasted several opportunities to make sure of the match before striker Saladin did late on.
Elsewhere, Tanzania came from a goal down to beat Gambia 2-1 at Dar Es Salaam.
Taifa Stars striker Mbwana Samatta believed the hosts needed victory after they had began their Group C campaign with defeat to Ivory Coast last week but they fell behind to Momodou Ceesay's seventh-minute strike.
They battled back gamely in the second half and Shomari Kapombe levelled proceedings on the hour mark before Erasto Nyoni's 84th-minute penalty settled matters.
Labama Kamana also struck late on from the spot to rescue a 1-1 Group H draw for Rwanda against Benin at Kigali.
Razak Omotoyossi's 74th-minute strike looked to have sealed all three points for the visitors but Kamana gave Rwanda a share of the spoils with his penalty two minutes from the end.
Lesotho and Sudan played out a goalless draw in Maseru in Group D while Mozambique and Zimbabwe also failed to score in their Group G clash at Maputo.