Justin Shonga hit a quick-fire brace in the final 10 minutes at Levy Mwanawasa Stadium as Chipolopolo booked their spot at the competition in Kenya with a 4-2 victory on aggregate.
The nations played to a 2-2 draw in East London last weekend.
Bafana Bafana assistant coach Thabo Senong guided the team in the absence of head coach Stuart Baxter, who stayed home to prepare for upcoming back-to-back World Cup qualifiers with Cape Verde.
Baxter's men will visit Cape Verde on September 1, with the return duel taking place four days later at Moses Mabhida Stadium in Durban (19h00 kick-off).
Bafana earned a 1-1 draw against Burkina Faso in Ouagadougou in October 2016 and followed it up with a 2-1 win over Senegal in Polokwane in November in their previous WC qualifiers.
Bafana: Bvuma (GK), Moleko, Khumalo, Booysen (c), Pietersen, Mntambo, Kumalo, Shongwe, Zuma, Ntshangase, Ntuli.
Subs: Hoffman (GK), Modise, Ndiki, Phohlongo, Meyiwa, Webber, Mabasa.