After Panama beat Martinique 3-0 in the earlier Group B game, the U.S. knew they needed to win by three clear goals to avoid a quarter-final match up against Costa Rica, one of the tournament favourites.
"Clearly a good result for us," said U.S. coach Bruce Arena. "It's a game where we wasted some opportunities and made things hard on ourselves," he added of his side missing two penalties.
The hosts took the lead after 36 minutes when Joe Corona's deflected strike got him on the international scoresheet for the first time in four years.
The Americans' second goal also came thanks to a deflection when Kelyn Rowe's shot outfoxed keeper Justo Lorente at his near post.
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Miazga got the crucial third, his first international goal, when he headed home a Graham Zusi free kick with two minutes remaining.
The Nicaraguans, who were already out the tournament after losing their first two games, were down to nine men at the time after they had Luis Copete sent off for two bookable offences, while another was receiving treatment on the sidelines.
The result was particularly harsh on Nicaraguan keeper Lorente, who saved second half penalties from Dom Dwyer and Corona.
The top two teams from each of the three Gold Cup groups advance to the quarter-finals along with the two best third-place teams.
In the only quarter-final match up already decided, Panama will face Costa Rica, while the U.S. must wait to find out who they face.
Canada and Honduras have also qualified.
Mexico, Jamaica and El Salvador are battling to qualify from Group C.
(Reporting by Andrew Downie; Editing by Greg Stutchbury)
