The hosts pushed their more illustrious opponents hard all the way, and had good scoring chances hitting the woodwork twice in the first half.
But Nigeria rallied to put some pressure of their own as both teams struggled in sweltering conditions.
Neither side managed to find any breakthrough and used up all three of their substitutions, but it was the Nigerian replacements that seemed the more impressive as they upped the tempo during the second half.
With the game petering away Everton defender Yobo popped up in a goalmouth melee to poke the ball home from close range and gave Nigeria all three points.
The win gives the Super Eagles six points from two games and keeps them top of the group above South Africa, who beat Equatorial Guinea 4-1 earlier in the day.
For Sierra Leone, the result leaves them in desperate straits and it is a toss-up as to when, not if coach Ahmed Kanu will be fired.