Ariel Martinez found Alberto Gomez for a 74th minute goal as Cuba picked up an unlikely 1-0 win and a date with the USMNT in the quarterfinals on Saturday.
A pair of desperate sides tangled in Charlotte on Wednesday, each knowing a tie or loss would send them out of the Gold Cup.
It was Guatemala that faltered.
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Last place Cuba had battled defections and visa issues en route to 6-0 and 2-0 losses to open the tournament, but came out with fire, picking up a pair of yellow cards within the first 17 minutes of play.
Guatemala was dominated by Mexico but picked up a point in a 0-0 draw, giving them hope of turning that positive result into something.
Cuba looked the better bet to score, especially as the match wore on. Headers were flicked just wide, and Paulo Motta foiled the Lions of the Caribbean as well.
That was until Gomez surged into the six to nail a header past the Guatemalan keeper.
Daniel Luis was offside on an 80th minute equalizer which would not stand for Guatemala.