Mexico are fielding a young, domestic-based squad at the bi-annual continental championship and their lack of experience showed as Gabriel Torres scored twice for Panama, who completed a day of upsets after Martinique's shock 1-0 win over Canada in the opening match of the 12-nation tournament.
Panama striker Torres put the underdogs ahead in the seventh minute at the Rose Bowl when he converted a penalty awarded after team-mate Alberto Quintero was brought down in the box.
Mexico recovered to take control of proceedings and deservedly levelled the contest just before half-time when Marco Fabian converted.
Torres, though, put Panama back in front just three minutes after the interval and they held on to complete the win and heap more pressure on coach Jose Manuel "Chepo" De La Torre.
Fabrice Reuperne was the match-winner, with the 37-year-old firing a left-footed blast from outside the box that found the top right corner of the net for the only goal of the contest and gave the Caribbean islanders a famous win.