The Super Eagles dominated possession but were unable to break down the resolute visitors.
The first half ended goalless.
Taiwo Awoniyi came on at the start of the second half to replace the injured Kelechi Iheanacho.
Osimhen, Awoniyi missed chances to put the Super Eagles ahead.
Central African Republic snatch the maximum points in the 90th-minute courtesy of a goal by Karl Namngandaa.
The second leg comes up in Cameroon on Sunday.