Guadeloupe beat Nicaragua 2-0 in the other Group C match to move top of the pool on a maximum six points from two games, two ahead of a disappointing Mexican side, who failed to build on Miguel Sabah's ninth-minute goal.
Panama responded well to the early setback and after forcing Mexican keeper Guillermo Ochoa into making a couple of good saves, Blas Perez equalised from a freekick in the 28th minute.
The match then descended into a volatile encounter with the first two dismissals coming on the stroke of halftime when Panama's Armando Gun received a straight red for wrestling Giovani Dos Santos to the ground.
He was joined by Mexico'S Luis Miguel Noriega, who was given his marching orders for his reaction to the challenge on his team mate.
In the 80th minute, Panama midfielder Ricardo Phillips and Mexico coach Javier Aguirre were also ejected after they became involved in a confrontation on the touchline.
Phillips initially refused to leave the pitch and protested the decision for more than five minutes before he was eventually persuaded to accept the red card, the delay leading to 10 minutes of added time at the end of the contest.
In the other match, Stephane Auvray and Ludovic Gotin scored second-half goals two minutes apart to send Guadeloupe top of the pool with a comfortable win over Nicaragua.
Guadeloupe and Mexico meet on Sunday to determine who will win Group C, while Panama (1 point) face off against Nicaragua (0 points).
The top two teams from each of the three groups and the two best third-place finishers advance to the quarter-finals of the 12-nation tournament.
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