The Black Maidens were close to winning it in regulation time before the 82nd minute before captain Nicole Perez whipped in a thunderous free-kick which flew past goalkeeper Buoadu for the leveller at 2-2.
Ghana captain Mukarama Abdulai gave the Maidens the lead in the 46th minute with a firm header on a cross from the right flank where Mavis Owusu was operating.
It was her seventh goal of the tournament in four matches to put her on top of the scorers chart.
But just after the hour mark, Mexico were awarded a penalty after a player was fouled inside the box by a Ghanaian defender.
Perez coolly picked her spot and converted the spot kick to level the scoring.
Substitute Susan Teye gave Ghana the lead again in the 75th minute with a fine finish just three minutes after coming on.
During the shootouts, Ghana missed two kicks from Tweneboah and Oppong out of four as Mexico scored all four.