Roared on by the home crowd at Rentschler Field in Connecticut, the United States were in control for most of the match and got the breakthrough in the 82nd minute when Landon Donovan found Brek Shea through the middle and he completed a nice left-footed finish.
Costa Rica finished the group in second place on six points and will meet Honduras in the quarter-finals, while the United States face El Salvador.
The United States were the only team to go through the group stage with three straight wins and are trying to win the Gold Cup for the first time since 2007 after enduring back-to-back defeats to Mexico in the 2009 and 2011 finals.
In the earlier Group C match, Jenier Marquez scored in stoppage time to seal Cuba's place in the quarter-finals with a 4-0 win over Belize.
Ariel Martinez had a hat-trick for Cuba but it was Marquez's last-gasp goal that took them through to the last eight of the Confederation of North, Central American and Caribbean Association Football regional tournament.
The Cubans needed to win by at least four goals to advance as one of the two best third-place teams in the competition.
Cuba led 1-0 at halftime after Martinez opened the scoring on 37 minutes then 2-0 midway through the second when the striker added a second.
There were just seven minutes left when the 27-year-old Martinez finished off his hat-trick.
The match was into injury time when veteran defender Marquez scored the crucial goal, enabling Cuba to leapfrog Martinique, who finished third in Group B, into Saturday's quarter-finals against Panama.
Mexico face Trinidad and Tobago in the last eight's other game.
(Editing by Peter Rutherford)
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