The richly-deserved win has left the Africans well-placed to qualify for the quarter-finals, with USA now likely to require a win against Japan - who play later this evening - in the sides' concluding Group D fixture.
The Americans had come into the game high on confidence from their thumping 6-1 win over Paraguay and that was evident from the assured way in which they eased themselves into this match. Ghana were pegged back throughout the opening exchanges and it was no surprise when, with five minutes played, BJ Snow's team took an early lead.
A well-worked goal it was too, with Civana Kuhlmann - scorer of a hat-trick in that opening-match win - this time in the role of creator. The USA No14 slipped a clever first-time pass through for Frankie Tagliaferri and, having sized up the angles, the midfielder arrowed a precise low shot in off the inside of the far post.
It was to Ghana's credit, though, that having lost heavily to Japan in their first Jordan 2016 fixture, they refused to allow their heads to drop. The Black Maidens rarely threatened during a forgettable first half but it was a different story after the break, when they began to lay siege to the American goal.
On more than one occasion, USA were indebted to goalkeeper Laurel Ivory, who was forced into alert saves to deny both Rafia Kulchirie and Sandra Owusu-Ansah. But when a goal did arrive to reward Ghana for their industry, it was the erstwhile flawless Ivory who was at fault. Adizatu Mustapha floated a high, hanging cross from the right and, when the US keeper misjudged it in her attempts to claim, Gifty Acheampong was left with a simple header into an empty net at the back post.
Snow's side were leaning against the ropes at this stage, but they very nearly restored their lead on 67 minutes when Ashley Sanchez rattled the crossbar with a ferocious 20-yard effort. The shot led to a bizarre moment with the ball hitting the woodwork, looping high in the air, dropping back down on the line and rebounding back the bar again before being gathered by Kanya Massey. Sanchez heard the referee's whistle and began to celebrate, thinking the ball has crossed the line, only to find out that it had spun out of play and a corner had been awarded.
Ghana, though, remained dangerous and it was no more than they deserved when they snatched a winner with six minutes remaining. This goal came from the penalty spot after another Mustapha cross was handled by Kiara Pickett, with Ivory guessing right and still finding herself unable to keep out captain Owusu-Ansah's precise and powerful side-foot finish.