El "Tri", who beat Jamaica on Thursday, reached six points to stay in first place in the tie, followed by Panama with four units.
"There are six very important points, as a visitor we were able to add three valuable points. It is a very important victory, Mexico was a fair winner, it was a very even game that was defined with a goal," said Argentine Jorge Theiler, Gerardo's technical assistant Martino.
"The key is that we have a group of players who are committed to making a good tie and being in the World Cup. All the group that accompanied Gerardo Martino are happy," added Martino's assistant.
The "Tata" Martino was not in the meeting because on Friday he underwent an operation on one eye.
In the match, which was played at the San José National Stadium, in Costa Rica, Mexico had the opportunity to open the scoring in the 20th minute when Andrés Guarded took advantage of an error by the Costa Rican defense, stole the ball and gave a pass. Rogelio Funes Mori, who was left unmarked in front of goalkeeper Keylor Navas, who deflected the Mexican forward's shot.
Mexico took the lead at the end of the first half with a penalty kick that Orbelín Pineda scored with a smooth and placed shot after Bryan Oviedo fouled Andrés Guarded inside the area.
In the final part of the game, Costa Rica pressed for the equalizer it came close to achieving in the 92nd minute with a shot from Keysher Fuller that crashed off the crossbar.
Costa Rica, led by Colombian Luis Fernando Suárez, is uphill with just one point from two games.
In the other qualifying games played on Sunday, Panama beat Jamaica 3-0 as a visitor with goals from Andrés Andrade, Rolando Blackburn and Cecilio Waterman.
Andrade scored the first in the 14th minute with a long-range shot that surprised goalkeeper Andrés Blake, Blackburn increased the lead in the 39th minute with a header from Eric Davis, and Waterman scored the third in the 81st after evading multiple players.
"You have to be humble, keep working and believing in what we are doing, I am generally happy for the team, it is important to see the commitment that the players have," said the technical director of Panama, the Danish Thomas Christiansen.
Meanwhile, the United States and Canada drew 1-1 with goals from Brenden Aaronson and Cyle Larin, respectively.
El Salvador and Honduras drew goalless in a match where Salvadoran goalkeeper Mario González became the hero after blocking Antony Lozano's header from a corner kick.
"In these two games we have achieved two draws with strong teams that have longer processes. We have to keep improving," said El Salvador technical director Hugo Pérez.
On the next round of the tie, to be played on Wednesday, Mexico will visit Panama, Costa Rica will be local to Jamaica, El Salvador will go to Canada, and Honduras will host the United States.
The first three places in the Concacaf octagonal qualify for the World Cup in Qatar. The fourth will have to play an intercontinental playoff in June 2022.