El Tri almost went ahead inside the opening five minutes after Israel Reyes picked out Jimenez on the edge of the penalty area, but his first-time finish was well parried by Ronwen Williams.
Mexico didn't need to wait long to break the deadlock, however, as Erik Lira won possession 20 yards out, and Quinones was able to run onto the ball and fire through Williams' legs after nine minutes.
Javier Aguirre's team continued to create the better chances before half-time, as Quinones hit the post with a low effort before Bryan Gutierrez sliced a shot wide after being played in behind by Quinones.
South Africa's hopes of getting back into the game were dealt a major blow early in the second half when Sphephelo Sithole was shown a red card for bringing down Gutierrez as the Mexico midfielder bore down on goal.
The points were made safe midway through the second period when Jimenez rose highest to meet Roberto Alvarado's cross and mark his first World Cup start with his a goal.
South Africa's misery was then compounded when Themba Zwane was sent off after he was adjudged to have hit Alvarado in the face, though Mexico captain Cesar Montes was also given his marching orders for a late foul on Khuliso Mudao.
GOAL rates Mexico's players from Mexico City...
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GOAL rates TEAM A's players from [STADIUM]...
