Jamaica, who were down to 10 men after a red card for Damion Lowe in the 47th minute, initially had the lead after stunning the visitors with a goal shortly after halftime.
Following a poor defensive clearance from El Tri off a corner, Jamaica's Daniel Johnson stepped up in the 50th minute and put the Reggae Boyz up 1-0 in Kingston's National Stadium.
After dominating possession in the first half, Mexico continued to amp up their pressure in the opposition's end of the pitch and began to create more dangerous opportunities.
That said, it was subtitutions from El Tri manager Gerardo "Tata" Martino that ended up making the difference.
Diego Lainez, Gerardo Arteaga, Jesus Corona and Henry Martin revived Mexico's energy as substitutes in the second half. Jamaica scrambled to hold onto their lead and began to quickly lose momentum as names like Corona and Lainez rushed further forward.
By the 81st minute, Martin equalized the scoreline at 1-1 after pushing the ball into the back of the net from close range.
Once the final whistle blew, Mexico not only secured three points, but also their first Octagonal round victory since October after suffering World Cup qualifying defeats to the United States and Canada in the previous window.
"We knew there was a long game ahead, we never lost our heads," said Vega to TUDN.
The win relieves some pressure on Mexico coach Gerardo "Tata" Martino, who reportedly reconsidered his role with the national team after the November losses to the U.S. and Canada.
"To the fans, I can only ask that they continue to support and trust us. We are looking for our best version," Martino said afterward.