Abby Wambach, the all-time leading scorer in women's football, added to her record total in the 45th minute and that was the only goal the Americans would need to finish the group phase unbeaten with a record of 2-1-0.
The Nigerian challenge faded in the 69th minute when the Super Falcons were reduced to 10 women after Sarah Nnodim was shown the red card for a clumsy challenge on Sydney Leroux.
Hope Solo collected her 173rd cap to pull level with Briana Scurry for most international appearances by a U.S. goalkeeper, while Wambach's 14th World Cup tally moved the American captain into a tie for second on the all-time list with Germany's Birgit Prinz.
In Edmonton, Australia (1-1-1) clinched the runnerup spot in Group D and a place in the round of 16 with a 1-1 draw with Sweden.
The Matildas went ahead in the fifth minute on a goal from Lisa De Vanna before Sofia Jakobsson equalised for the Swedes 10 minutes later.
Fifth ranked Sweden (0-3-0) could yet advance with the four best third-place finishers of the tournament also qualifying for the knockout.
(Editing by Andrew Both)
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