A 2-1 victory in Botswana for Ethiopia means they are also in line to secure a place in the final phase of the African preliminaries if they win again next weekend.
First-half goals from Getaneh Kebede and Saladin Seid, his fourth of the campaign, kept Ethiopia top of Group A with 10 points from four matches.
They are two points ahead of 2010 World Cup hosts South Africa, their next opponents.
Ethiopia qualified for the 2013 African Nations Cup after an absence of more than three decades and proved difficult opponents in the finals.
South Africa won 3-0 in the Central African Republic to keep alive their hopes in a match played in neutral Cameroon because of the precarious situation in Bangui where the government was recently overthrown by rebel fighters.
Congo and Tunisia lost their 100 percent records but away draws inched them closer to winning their respective groups.
Giant defender Christopher Samba withdrew on the eve of the game but Congo held neighbours Gabon to a 0-0 draw in Franceville to earn a six-point lead over their second-placed opponents in Group E.
Third-placed Burkina Faso, on three points, can close the gap when they play in Niger on Sunday.
A late equaliser from Fakhreddine Ben Youssef gave Tunisia a 2-2 draw at closest challengers Sierra Leone and a five-point lead in Group B.
The Tunisians can clinch top spot by winning in Equatorial Guinea next weekend.
African Footballer of the Year Yaya Toure was among the scorers as Ivory Coast triumphed 3-0 in Gambia to take their points tally in Group C to 10 from four games.
Morocco also beat Tanzania 2-1, leaving the Ivorians four points clear with two matches to play.
Zambia retained their one-point lead over 2010 World Cup quarter-finalists Ghana in Group D after sinking Lesotho 4-0.
Ghana won 3-1 in Sudan on Friday with two goals from Asamoah Gyan.
Papiss Cisse put Senegal ahead in Angola in Group J but Guilherme Afonso equalised to earn a 1-1 draw, the fourth in as many matches for his team.
Senegal lead Uganda by one point with Angola and Liberia one point further back.
Six more qualifiers will be played on Sunday.
The 10 group winners go through to the playoffs in October and November to determine the five African qualifiers for Brazil 2014.