Adebayor, who had been out for six weeks with a hamstring problem, took advantage of an 11th-minute slip by defender Andre Bikey to settle the opening Group A game in the final round of African qualifiers.
The African Footballer of the Year went on to complete the 90 minutes in Accra but blotted his copybook by missing a second-half penalty.
The match was played in neighbouring Ghana because Togo are banned from using their home ground after rioting two years ago.
Gabon went joint top in Group A after a shock 2-1 victory in Morocco.
Teenage debutant Pierre-Emerick Aubameyang scored in the 34th minute and Roguy Meye doubled the lead before halftime.
Morocco’s goal came from Dutch-born Mounir El Hamdaoui near the end.
In Group E, Moumouni Dagano took his qualifying campaign tally to nine goals with a double in Burkina Faso’s 4-2 triumph over Guinea in Ouagadougou.
Dagano converted a 53rd-minute penalty and scored again 13 minutes later.
In Group D, Frederic Kanoute netted in Mali’s 1-1 draw with Sudan in Khartoum.
Kanoute struck in the 20th minute but Sudan, led by English coach Steven Constantine for the first time, equalised three minutes later through Mudathir Taher.
In Group B, Tunisia recorded a 2-1 victory over Kenya in Nairobi.
Issam Jemaa grabbed the 72nd-minute winner, two minutes after Kenya had equalised with a tap-in from Dennis Oliech.
Earlier, Tunisia went in front in the fifth minute when a defensive error allowed Ammar Jemal to score.
In Group C, Rwanda and Algeria shared a goalless draw in Kigali.
Nigeria’s Group B game in Mozambique is one of four qualifying matches scheduled on Sunday.