In the other group game, Kenya lost 1-0 Sunday at Mozambique, with Tico Tico scoring the only goal of the game midway through the second half.
Nigeria, who are second in the group on six points, have to rely on the help of either Kenya or Mozambique if they still want to catch Tunisia, who have eight points with just two matches remaining.
Mozambique are on four points, while Kenya have three.
In Group C Egypt remain in contention after winning 1-0 Saturday in Rwanda through a goal by substitute Ahmed Hassan. The midfielder scored on a cross from Ahmed Fathi to keep alive the Pharaoh's hopes of making it to South Africa.
Algeria, though, are favourites to qualify from the group and can move three points ahead if they beat Zambia at home in Sunday's late match. Algeria, like Egypt, are on seven points but have a game in hand. Zambia are on four points, while Rwanda have one point.
In Group E, the Ivory Coast are within a point of qualifying after hammering Burkina Faso 5-0 Saturday in Abidjan.
The home side took the lead in the 12th minute through an own goal by Saidou Panendetiguiri.
Chelsea's Didier Drogba added two more in the second, and Barcelona's Yaya Toure and Abdel Kader Keita also found the net.
The other game saw Malawi win their first game in the final qualifying stage Saturday in Blantyre with a 2-1 comeback victory over Gabon, who took the lead in the 37th minute through Oumar Kalabane.
Substitute Chiukepo Msowoya, who came on at half-time, equalised just two minutes into the second half and found a second in the 58th minute to give his side a win that keeps them in contention for a place at the Nations Cup.
The Ivory Coast have 12 points from four games, while Burkina Faso are on six points. Guinea and Malawi are both on three points.
The five winners of the groups will qualify directly for the World Cup and African Nations Cup finals, while the second and third placed teams qualify for the Nations Cup finals.