Meanwhile, South Korea were condemned to an early exit after losing their opening two matches despite Heung-Min Son scoring a spectacular consolation strike in stoppage time.
Mexico were looking to build on their famous victory over the defending champions Germany in the group opener and, after a slow start this weekend, Javier Hernandez headed wide from a free-kick by Hector Moreno.
Mexico were awarded a penalty in the 24th minute when Jang Hyun-soo handled a cross from Andres Guardado, however, and Carlos Vela converted from the spot to send his team 1-0 ahead in the 26th minute.
The hapless Koreans, who have no points after two matches and have only won one of their last 11 World Cup fixtures, will be eliminated if Sweden draw or win against Germany.
Vela and Hirving Lozano also had chances for Mexico, before the second goal arrived with 25 minutes to go through Mexican all-time top scorer Hernandez.
But, six minutes before the half-hour mark, El Tricolor were handed the flawless opportunity to open the scoring when opposition defender Jang Hyun-soo needlessly went to the ground in an attempt to block an Andres Guardado cross - only to handle the ball inside the area.
Kim Jong-un visits China after Trump summit
The visit would also serve to underline that Kim is adhering to a request made by Xi at their first meeting in Beijing . President Richard Nixon and Chinese leader Mao Zedong, resulting in a fundamental reorientation of Sino-U.S. relations.
Gregg Popovich meets with disgruntled Kawhi Leonard
Leonard is under contract for two more seasons but can exercise a player option to become an unrestricted free agent next summer. The 26-year-old Leonard is reportedly angry over the handling of his injury and comments from Tony Parker and Popovich.
Denmark frustrated by Australia in World Cup draw
The Danes previously beat Peru, while Australia lost to France. "We're still in with a sniff", said Jedinak after the game. Christian Eriksen scored in the opening minutes for Denmark , which has gone unbeaten in 17 straight global matches.
Democratic women win big in key Virginia House primaries
Rachel Talbot Ross, a Democrat representing Portland's District 40, fended off in a primary challenge from former Rep. Longtime Register of Deeds John O'Brien of Lynn also will be facing a Democratic primary challenge in September.