Leon Balogun atoned for his costly mistake in defeat to the Wild Beasts by opening the scoring in the 29th minute of the match in Cameroon.
The defender provided a striker's finish after staying up-field and profited from a precise Chidozie Awaziem cross to fire the visitors in front.
The Super Eagles made it two before the break as defensive partner William Troost-Ekong found Victor Osimhen who finished with aplomb from close range to build on his impressive scoring record at international level.
This forced the hosts into a change of approach after the interval but Nigeria held firm and they will go into the November round of qualifiers holding at least a two-point lead with two matches remaining.
Central African Republic (0) 0
Nigeria (2) 2 (Balogun 29' Osimhen 45+1')
CAR: Samolah; Ngam-Ngam, Ndobe, Ban (Ndambakizi 54'), Yangao, Guinari, Toropite (Grengou 79'), Urie (Namnganda 54'), Niamathe, Gaopandia (Kpeko 79'), M'Vondo Ze (Ngoma 46').
NIGERIA: Okoye; Balogun (Omeruo 74'), Troost-Ekong, Collins, Awaziem, Ayodele-Aribo, Onyeka, Musa (Ejuke 67'), Simon, Iheanacho (Innocent 74'), Osimhen.