Bethany England, Rachel Daly, Alex Greenwood and Chloe Kelly all scored in Brisbane as England survived the sending off of Lauren James in normal time to progress.
Georgia Stanway and Desire Oparanozie sent their opening sides penalties wide of the post before Michelle Alozie also missed the target for Nigeria to leave England in control.
James was sent off for a reckless stamp with four minutes of the 90 remaining, planting her studs on the back of Alozie.
The 21-year-old Chelsea forward was England’s star player in the group stage, scoring the winner against Norway and bagging a double in the 6-1 thrashing of China, but she was well-shackled by Nigeria and allowed her frustration to boil over.
James was initially shown a yellow card but it was changed to a straight red after referee Melissa Borjas checked her pitch-side monitor on the recommendation of the VAR.
Her dismissal left England facing spot-kicks to avoid another massive shock at the tournament, which had already seen former winners USA and Germany eliminated early, along with Brazil. James will miss the quarter-final against on Saturday.
Nigeria outplayed England over the 90, twice hitting the crossbar, and had the better of extra-time, although both sides visibly tired.
Alessio Russo and Daly both drew smart saves from goalkeeper Chiamaka Nnadozie, while England were awarded a first-half penalty for a shove on Daly — which was overturned after Borjas checked her monitor.
England remain among the favourites for the tournament, while Nigeria were aiming to become the first ever African nation to win a knockout game at the finals.