The win leaves the Reggae Boyz still searching for their first goal and unable to go through, with Uruguay also knocked out after losing to Venezuela, the other qualifiers in Group C.
But the match was mired in controversy as Jamaica were denied a spot-kick and a chance to equalize in the second half after striker Clayton Donaldson looked to have been fouled in the area.
The game had kicked off in a carnival atmosphere generated by a 83,263 crowd made almost entirely of Mexico fans.
Jamaica had named a makeshift back line that was missing the injured Kemar Lawrence and tough-tackling Rodolph Austin.
The team were also sorely missing the influence of head coach Winfried Schaefer, who was suspended after being sent to the stands in the opener.
Their inexperience showed in the 18th minute as Jesus Manuel Corona was allowed to float in a cross from the left to an unmarked Javier Hernandez, who nodded in from six yards for what will be one of the easiest of his 45 international goals.
The prolific former Man Utd and Real Madrid striker is now just one off equaling Mexico’s all-time scoring record, held by Jared Borgetti.
Jamaica had most of the early chances and should have drawn first blood on five minutes when Donaldson found himself in space in the area, only to hook his shot for a goal kick.
The Birmingham City striker was profligate again on the half hour, heading wide before his team mate Garath McCleary fluffed a perfect pull-back by Jobi McAnuff.
Jamaica had another golden opportunity to draw level before half time but Malaga goalkeeper Guillermo Ochoa showed incredible reactions to fend off Michael Hector’s blasted shot from point blank range.
Mexico were inches away from putting the match beyond Jamaica soon after the break, when a sweet pass from Corona found Jimenez at the far post.
The striker’s volley bounced deliciously across the face of an open goal, but it was just beyond the oncoming Hernandez.
Mexico began turning the screw, attacking in waves but couldn’t find a way through and were caught on the break on 60 minutes when Donaldson took the ball around a defender only to be cut down by Yasser Corona.
Replays showed the defender didn’t get a touch on the ball, but Brazilian match official Wilton Sampaio looked away and there were few complaints from the partisan crowd.
Jamaica’s misery was sealed when Mexico’s Hirving Lozano picked out Hector Herrera in the area and the midfielder nudged the ball on for substitute Oribe Peralta to stroke the ball first time inside the right hand upright on the 81st minute.