After the save, Adalberto Carrasquilla then scored against Matt Turner to win the shootout 5-4 against the defending champions. Mosquera also made a save against Jesus Ferreira, while Turner stopped Cristian Martinez.
The match was goalless for 90 minutes before Ivan Anderson gave Panama a 1-0 lead in the ninth minute of extra time. Ferreira then made it 1-1 six minutes later.
The US had just one chance in the opening half, and that came 24 seconds into the match when Cade Cowell, in his first Gold Cup start, hit the post.
Panama enjoyed 56% of the possession, but the Americans still managed to go toe-to-toe with the visitors in what was a relatively even game.
Early in the second half, Turner made an outstanding reactionary save to stop a powerful header by Ismael Diaz, and the US dodged a possible penalty in the fourth minute of stoppage time when VAR determined that Djordje Mihailovic did not commit a handball.
Anderson chipped the ball over an onrushing Turner, who stepped outside the box, and rolled the ball into the empty net early in extra time before Ferreira, who had back-to-back hat tricks in the group stage, scored on the volley after Jordan Morris headed the ball to him.
It was looking similar to the US match against Canada in the quarter-finals this past Sunday, when the Canadians went up 2-1 in extra time before the Americans got the equalizer and won the penalty shootout with two Turner saves.
This time though, they were on the losing end of the spot-kicks.
Panama will play the final on Sunday in Inglewood, Calif., against Mexico, who beat Jamaica 3-0 later Wednesday night.
