The matchday 5 point lifted the Carthage Eagles to 11 in Group G and ensured them of a top-two finish and qualification for the January 17-February 8 finals in Equatorial Guinea.
Algeria and Cape Verde Islands booked places at the three-week tournament last month.
Egypt host Senegal Saturday in the other Group G fixture and with just one point separating the sides, the result could determine who accompanies Tunisia.
Forcing a draw at the national stadium in Gaborone meant Botswana ended a run of four consecutive group losses that began with a 2-1 defeat in Tunisia two months ago.
Ivory Coast boosted their chances of reaching the biennial African football showcase by thrashing Sierra Leone 5-1 in Group D at Stade Felix Houphouet-Boigny in Abidjan.
Former Chelsea striker Salomon Kalou bagged a brace and Liverpool defender Kolo Toure, Max-Alain Gradel and Gervinho also scored for the Elephants.
A mid-first-half Mustapha Bangura goal levelled the score after Toure — older brother of reigning African Footballer of the Year Yaya Toure — struck on seven minutes.
The second half was one-way traffic toward the goalmouth of the Leone Stars, who were forced to concede home advantage because of the Ebola epidemic.
Ivory Coast are second with nine points, one behind Cameroon and three ahead of the Democratic Republic of Congo, who play in Yaounde Saturday.
There are 12 qualifiers scheduled for Saturday with defending champions Nigeria needing a victory in Congo Brazzaville to have a realistic chance of qualifying.
Equatorial Guinea were named the new hosts Friday, replacing disqualified Morocco.
The Moroccan government wanted the Cup postponed because of the Ebola epidemic, which has claimed more than 5,160 lives this year, mostly in Liberia, Guinea and Sierra Leone.