Cox ran onto an attempted sliding clearance by Cuban defender Yarisleidy Mena, and stuck the ball first time at the restraining arc to beat Cuban keeper Dainelis Moreno in the 54th minute.
The match was relatively even through the first 45 minutes, with both sides scoring on remarkable individual efforts. But with the humidity climbing throughout the game to reach 74 percent and temperatures still at 81 degrees Fahrenheit (27 Celsius) by the second-half kickoff, Cuba - with only four available substitutions ---- seemed to be hampered more significantly by cramping, enabling Panama to take control.
Panama, making its fourth appearance at the CONCACAF finals but first since 2006, won for the first time since beating Jamaica 2-0 in 2004.
Cuba had the better of early play, sending a cross through the area that was deflected out for a corner in the third minute.
But Panama slowly gained the momentum and went ahead in the 16th when Angela Evans picked up a loose ball at the top of the defensive third, took a touch and unleashed a right-footed drive that sailed just over the outstretched arm of Cuban keeper Dainelis Moreno.
Cuba began to mount some offense of its own but equalized on a 65-yard run by Rachel Paleaz. With her back to goal, Pelaez received the ball just inside the center circle in the Cuban half, turned and sprinted past four defenders into the Panamanian penalty area before hitting a right-footed shot inside the far post and past diving keeper Dayton Wetherby.
Cuba lost for the seventh time in as many games at the CONCACAF finals, and scored only its fourth goal.
It will try again for its first victory on Sunday against the two-time and defending champion United States, while Panama will face Central American rival Guatemala. The United States beat Guatemala 6-0 in the first game of Friday's doubleheader.