The 27-year-old struck a 61st-minute winner as Ethiopia came from a goal down against Central African Republic to secure their place in Africa's 10-team play-off round.
Teshome had been the player at the heart of the controversy that had threatened Ethiopia's progress, after they were docked points for fielding the midfielder when he should have been suspended in June's qualifier against Botswana.
That penalty meant Ethiopia's place would have only been assured by victory in Brazzaville - with South Africa coasting past Botswana 4-1.
But the Bafana Bafana's result was deemed meaningless as Salahdin Ahmed (48) and Teshome (61) struck after Salif Keita had given the hosts a 23rd-minute lead.
Bernard Parker (84, 89) scored twice for South Africa after Kermit Erasmus (28) and Dean Furman (45) had fired the 2010 World Cup hosts into a 2-0 half-time lead.
Jerome Ramatlhakwana scored Botswana's only goal 17 minutes from the end.
Nigeria progressed on the back of a 2-0 win over Malawi.
Emmanuel Emenike beat the offside trap to open the scoring in first-half injury-time before Victor Moses' placed penalty six minutes after the restart sealed the win.
Ghana, Algeria, Egypt and Ivory Coast have already secured their place in the next stage - where the winners of the five two-legged ties will book their place at the World Cup finals.
Burkina Faso jumped ahead of Congo in Group E following a 1-0 win against Gabon in Ouagadougou.
Prejuce Nakoulma scored the goal to send Burkina Faso through on 54 minutes after Congo could only draw 2-2 away to Niger.
Congo twice battled back from behind, Fabrice Nguessi (66) and Ulrich Kapolongo (76) cancelling out goals from Mahamane Cisse (34) and Daouda Kamilou (7), but the winner the visitors needed never arrived.
Cape Verde Islands upset Tunisia 2-0 in Rades to move above the north Africans and progress as Group B winners.
Platini opened the scoring on 28 minutes with Nhuck adding a second three minutes before half-time.
Sierra Leone ended their campaign with a 3-2 home win over Equatorial Guinea.
Senegal seal their place in Group J with a 1-0 win over 10-man Uganda.
Godfrey Walusimbi saw red on 36 minutes and Senegal eventually made their extra-man advantage tell through Sadio mane six minutes from the end.
Ivory Coast, already through, drew 1-1 at home to Morocco after Didier Drogba's late penalty cancelled out Youssef El Arabi's 53rd-minute opener. Mustapha Jarhue struck twice as Gambia beat Tanzania 2-0.
Cameroon and Libya will met in Yaounde on Sunday to confirm the final qualification place in the play-off round. Cameroon need only avoid defeat to progress.