Mexico had their second of the game in the 66th minute, however, when Hernandez collected a super pass from Lozano before finishing low into the bottom corner of the net to register his 50th global goal. Son Heung-min pulled one back for South Korea in stoppage time with a spectacular left-foot strike from outside the area.
If Mexico's qualification isn't confirmed today, the national team will have the chance to determine its own fate in its third and final group match against Sweden in Ekaterinburg on Wednesday.
Juan Carlos Osorio's team dominated possession in the opening stages, and took the lead from the penalty spot on 26 minutes after Andres Guardado's cross into the box was clearly handled by a sliding Jang Hyun-soo.
The momentum Mexico can build with another win might carry El Tri deep into the 2018 FIFA World Cup.
South Korea coach Shin Tae-yong stuck to his attacking line up but shook up his midfield with Ju Se-jong and Moon Seon-min coming in for Park Joo-ho and Koo Ja-cheol, as the 2002 semifinalists seek to recover from their opening 1-0 loss to Sweden.
"We have beaten two brilliant and complicated teams, Germany and South Korea", Hernandez said. A volley from Vela skimmed the bar minutes later.
Then, only 25 minutes into Saturday's game, Mexico scored its first goal, taking an early 1-0 lead. Six of the penalties were awarded after video reviews.
Ki Sung-yueng threatened in the 56th minute with a ferocious drive that Guillermo Ochoa could only gather at the second attempt, before Cho did well two minutes later to keep out a curler by Guardado at full stretch. He hit the ball low past goalkeeper Jo Hyeon-woo after collecting a pass from Hirving Lozano.
While Mexico hasn't yet technically qualified for the last 16, if Sweden draws with or defeats Germany in the match now under way in Sochi, its spot in the second round will be confirmed.