France — who have not been beaten inside 90 minutes in a World Cup knockout match since the 1986 semi-finals — will play either Germany or Algeria in Rio de Janeiro on Friday.
Nigeria — bidding to reach the quarter-finals for the first time — had the ball in the net in the first-half but the linesman flagged for offside against the scorer Emmanuel Emenike.
France’s best early chance saw Pogba’s effort brilliantly saved by Vincent Enyeama.
However, Pogba was to benefit from a rare error by Enyeama as he flapped at a corner and the ball fell nicely onto his head and he finished it off to give the French the lead 11 minutes from time.
Yobo’s own goal came in time-added on stemming from another brilliant set piece by France’s most eyecatching player Mathieu Valbuena.