Quiñones broke the deadlock after just nine minutes, capitalising on a giveaway by South Africa midfielder Yaya Sithole to beat goalkeeper Ronwen Williams from inside the box. Jiménez doubled Mexico's lead in the 67th minute, converting a header from a Roberto Alvarado cross — his first World Cup goal.
Sithole was sent off in the second half for denying Bryan Gutiérrez a clear goalscoring opportunity. Teammate Themba Zwane followed for a second South African red card, and Mexico finished the match with ten men themselves after César Montes was also dismissed — meaning the Wolverhampton Wanderers defender will miss Mexico's next group fixture.
South Africa manager Hugo Broos addressed the red cards directly afterwards.
"The first red card, I don't think we have to say something about it but the second red card I think the Mexican player blocked my player, that happens, the referee decides something else so it is a little bit a pity that we have to finish this game with nine players."
Broos found things to be positive about despite the result.
"I think my team played a good game, some moments in the game Mexico were even desperate, they didn't know how to find the spaces so everything was good. The only thing that must be better in the next game is when we have the ball. That was not so good today so we have to work on it."
Quiñones, a Colombian-born forward whose 2023 Mexico debut drew criticism in some quarters for his lack of Mexican heritage, described the emotion of scoring the first goal of the tournament.
"Many things came into my head like celebrating and screaming with joy. I went to the bench to see my peers because they have given me so much confidence. I wanted to feel that joy with them."
He also reflected on the red card to teammate Montes.
"There were some mistakes that were very costly. Being sent off is something you can avoid."
On Jiménez's milestone goal, Quiñones was warm.
"We really congratulated him because he gives a lot to the team. Being part of a team is our pride and it's wonderful he continues to add goals to his career as a player in our national team."
Alvarado, whose cross set up the second goal, described the occasion in personal terms.
"It was a really beautiful feeling, something beyond words, something I had always dreamed of: playing a match of this magnitude, at home, with these fans."
He explained the thinking behind the assist.
"At half-time, he had told me to send in a cross for him. I didn't think twice, and I knew that in that area it could be dangerous. Thank God I got the assist and Raul was able to score that goal."
Alvarado also offered a measured assessment of the performance as a whole.
"The game plan is always to go out and press. After that, we dropped the tempo a bit, but maybe we lacked a little more patience and a little more possession of the ball."
Mexico top Group A after matchday one. Montes's suspension leaves a gap at centre-back for the next fixture — a problem for another day in a tournament that has, in its opening match, already delivered more drama than most entire group stages.