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The opening goal by Quiñones marked his third score of the competition, making him the tournament spark for Mexico.
The 29-year-old forward moved from Colombia at age 17 and became a naturalized Mexican citizen in 2023.
"I am just happy with the result, that is all that matters now," said Quiñones.
Quiñones is currently playing in his first career World Cup with the Mexican national team.
"Life is about struggle and fight until you get what you want," he said, "and I am taking full advantage of the opportunity that I got."
The second goal by Jiménez brought his international tally to 47 goals, breaking a historical tie with Jared Borgetti.
Jiménez is now five goals away from matching Javier "Chicharito" Hernández as the all-time leading goalscorer for the national team.
The result also establishes Mexico as the first CONCACAF nation to eliminate a CONMEBOL team during a World Cup knockout match, breaking a five-game winning streak held by South American teams.
Additionally, the victory extends Mexico's unbeaten streak to 12 games across all competitions.
A severe thunderstorm delayed the kickoff at Azteca Stadium by one hour, marking the second weather delay of the tournament.
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Mexico will next play a home match on Sunday against the winner of the fixture between England and Congo.
