Martinez had previously seen a penalty claim dismissed by the referee after going down in the box under pressure from Jerome Opoku.
Ghana also generated chances later in the game when Jonas Adjetey executed a powerful header that required a smart save from Panama goalkeeper Orlando Mosquera.
Shortly after, Thomas-Asante sent a low cross toward Jordan Ayew, but Panamanian defender Jiovany deflected the ball just wide of the post.
The match also featured two hydration breaks amid light rain, both of which drew loud boos from the spectators.
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Ghana will next face England in Boston on June 23, while Panama is scheduled to play Croatia in Toronto on the same day.
