It was Mexico's first win in the final stage after three straight draws and put them top of the six-team group on six points, while Jamaica, who host the United States on Friday, are bottom with two points from four games.
The first half of Tuesday's game echoed the 0-0 draw at the Azteca stadium in February. Mexico enjoyed the bulk of possession but failed to create real chances, while Jamaica were well-organised and hard working but missing a spark.
The nearest either side came to a goal before the interval was a low drive from Mexican striker Javier Hernandez which skidded inches wide of goalkeeper Donovan Ricketts' post.
The breakthrough came three minutes after half time when Carlos Salcido burst down the left and whipped in a beautiful cross which De Nigris met with a powerful header.
The goal opened the game up and Jamaica twice forced Mexico keeper Jesus Corona into action.
First Corona made a fine stop with his legs after a dangerous cross from Jermaine Hue was deflected goalwards, and then from the resulting corner he got down well to push a Marvin Elliott header wide.
At the other end, Ricketts rushed out well to foil Hernandez but Jamaica continued to press and should have scored when Elliott miscued a header from close range.
Substitute Giovani dos Santos then found Hernandez with a sweeping cross-field pass but again Ricketts was up to the task and palmed the low shot wide.
Mexico travel to Panama on Friday before heading to Brazil for the Confederations Cup.
The top three teams from CONCACAF qualify automatically for the World Cup finals next year in Brazil with the fourth-placed side taking on New Zealand in a two-legged game for a spot in the finals.
Mexico currently lead with six points, Panama have five and Honduras, the United States and Costa Rica all have four points.
