Mexico looked to have broken the deadlock in the 33rd minute but Henry Martin's goal was disallowed for offside after a VAR review. They had another excellent opportunity just before the break but Panama keeper Orlando Mosquera denied them again.
Panama’s Harold Cummings was shown a second yellow card in the 63rd minute but the referee reversed his decision after it was determined there was no contact on the play.
Panama's best chance came in the 87th minute but Edgar Barcenas' long-range shot sailed wide of goal.
Gimenez, who had only been on the pitch a few minutes, then came up with the only goal of the game.
Edson Alvarez found him near midfield before the 22-year-old raced past two defenders and slotted home with his left foot for an 88th-minute winner that sent the sold-out crowd at SoFi Stadium into a frenzy.
"It is indescribable," Argentina-born Gimenez said after the match.
"The only thing I feel is love and passion for those who are always there. God, my family and the people who came today, 75,000 people. We had to give them this Cup."
The victory was a welcome one for Mexico, who had failed to make it beyond the group stage at last year's World Cup. It also denied underdogs Panama, who upset the United States in the semi-finals, their first Gold Cup title.
Mexico will hope the win marks a new chapter for the team, who are being led by Jaime Lozano after Diego Cocca was fired following last month's Nations League.
