Gonzalez's first error came when he misjudged a deep cross from Mexican captain Rafael Marquez in the 19th minute and flapped the ball into his own net.
Marquez, who earlier this month joined Catalan club Barcelona from French first division side Monaco, said his goal was one of the weirdest he had ever scored.
"I wanted to put over a centre and I surprised him and also surprised myself," said Marquez, who sat out the second half on the bench with an ice pack over his left knee after picking up a slight injury.
The Costa Rican keeper compounded the mistake by spilling a low-driven free kick by Rafael Garcia that allowed striker Jared Borgetti to tap in the rebound with Gonzalez floundering on the floor, giving Mexico a 2-0 lead in the 28th minute.
It was an advantage that Mexico rarely looked like losing.
The bizarre first goal took the wind out of Costa Rica who until then had created the better chances.
In a five-minute spell, the busy Walter Centeno hit the bar with a long range shot with Mexican goalkeeper Oswaldo Sanchez beaten.
Centeno, who plays with AEK
Costa Rican striker Winston Parks whipped a right foot shot across the Mexican goal that Sanchez palmed wide.
A scrappy second half, towards the end played in torrential rain, saw Costa Rica come back into the match, especially with the inclusion of the striker Rolando Fonseca.
But there were still few clear chances on goal.
In injury time, Fonseca had Costa Rica's best chance to pull a goal back but his low shot was again well saved by Sanchez, who has yet to allow in a goal in Mexico's four matches to date in the tournament.
Midfielder Pavel Pardo, who slipped on the captain's armband for the second half, was pleased to reach the final.
"We won well, played well and we are happy to be going to the final, but we have not won anything yet," he said.
Mexico face Brazil in Sunday's final in Mexico City -- a repeat of the sides's opening game in this year's cup, which Mexico won 1-0.
Brazil's team is its under-23 selection, with stars like Rivaldo, Ronaldo and Ronaldinho not playing.
Costa Rica meet the United States in the third place playoff on Saturday in Miami, a replay of the 2002 Gold Cup final that the United States won 2-0.
