Abby Wambach's volley just before the break proved enough for the US, but they could not add to their lead despite Nigeria losing defender Sarah Nnodim to a second yellow card.
They will play one of four third-placed teams to progress from the pool stages.
Australia secured Group D's second spot with a 1-1 draw against Sweden.
The Matildas will play Brazil in the next round in Moncton.
Meanwhile Sweden, ranked fifth in the world, will have to wait to see whether they claim one of four qualifying spots for teams finishing third in their group.
Australia took the lead after just five minutes as captain Lisa De Vanna sprinted onto a long ball forward and coolly slotted home.
But any hopes they had of overhauling the United States at the top of the group were reduced as Sofia Jakobsson levelled 10 minutes late with a low shot inside goalkeeper Lydia Williams' near post.
In Edmonton, the 14th World Cup goal of Wambach's career - an instinctive far post volley from Megan Rapinoe's corner - proved enough for the United States.
But Nigeria coach Edwin Okon was left aggrieved by the referee's decision to issue Nnodim with a second yellow for a challenge on Sydney Leroux that left his side down to 10 players for the final 20 minutes.