The game looked headed for extra time before Pogba broke the deadlock in the 79th minute at the Mane Garrincha National Stadium, reports Xinhua.
Nigeria’s Norwich City defender Yobo then unwittingly deflected in France’s second goal in injury time.
France will now play either Germany or Algeria at Rio de Janeiro’s Maracana stadium July 4, with a place in the semifinals at stake.
The result continues the remarkable record of Les Bleus’ coach Didier Deschamps in football’s premier event.
The former France captain is unbeaten in 10 World Cup matches as both a player and manager.
Despite entering the match as rank underdogs, Nigeria looked vibrant early.
Peter Odemwingie will have rued his missed opportunity in the fifth minute when he failed to connect with an attempted volley after a cross from the right found him free in the penalty area.
Odemwingie was again involved shortly after, providing a sumptuous delivery from a set piece to John Obi Mikel at the far post. But the Chelsea midfielder’s tame header did not trouble France goalkeeper Hugo Lloris.
Les Blues began to find their rhythm after the quarter hour and Olivier Giroud shot over the bar after a smart turn at the top of the penalty box.
France’s best attempt of the first half came from Pogba. The Juventus midfielder laid the ball off for Mathieu Valbuena, whose cross from the right again found the former Manchester United man.
But his fierce first-time shot drew a sharp reflex save from Vincent Enyeama.
Mathieu Debuchy then sprayed his shot wide after Blaise Matuidi’s neat build-up play with Valbuena.
Nigeria almost made France pay for their profligacy on the stroke of halftime when Emmanuel Emenike wandered unmarked to the edge of the area before unleashing a powerful shot that Lloris palmed clear.
Nigeria began the second half as they had the first: with greater possession and menace around the final third.
Deschamps replaced the ineffective Giroud with Antoine Griezmann and the Real Sociedad forward provided an immediate spark.
His neat one-two with Karim Benzema sent the Real Madrid forward clear on goal but his chipped effort was cleared off the line by Victor Moses.
Griezmann again exposed Nigeria’s defence when his cross to the edge of the six-yard box forced a lunging clearance from Enyeama.
The Super Eagles were under siege and France were denied once more as Benzema’s header from a Valbuena free-kick was finger-tipped over the bar by the hitherto impressive Enyeama.
But despite his heroics, the Nigeria goalkeeper was largely to blame for France’s first goal.
His bungled clearance from a Valbuena corner allowed Pogba to head the ball into an unguarded net.
Griezmann nearly doubled France’s lead but his powerful shot after a blazing run into the area was spectacularly parried away by Enyeama.
The result was then put beyond doubt when Yobo deflected Valbuena’s delivery into his own net.