Substitute forward Javier Hernandez beat an offside trap, raced into the box unchallenged and twisted his way past France keeper Hugo Lloris to put Mexico ahead on 64 minutes.
Wily forward Cuauhtemoc Blanco, 37, doubled the advantage from the penalty spot on 79 minutes after Pablo Barrera was brought down by Eric Abidal, sending his country's fans wild with delight in a contrast to the glum French faces.
"I'm delighted. The goal is for the whole country," Hernandez told a news conference as cries of "Ole!, Ole!" from the jubilant Mexican fans could be heard outside.
"Whoever scored first was going to win. The goal made us feel calm," the former Mexico international told reporters, expressing his pleasure that the team's style of bombing forward had paid off.
"We always try to be audacious to put the ball in the net. We do run risks," he said.
Mexico's Achilles heel in the first game - the lack of a killer instinct in front of goal - was again threatening to hinder their progress until Hernandez's timely strike.
Not long after, first half substitute Pablo Barrera's searing run into the penalty area ended with a foul by Abidal and Blanco smashed home the resulting penalty in emphatic fashion for his 39th goal for his country.
"I'm lost for words. It's a real disappointment for those who believed in us," France coach Raymond Domenech told French television channel TF1.
"There's one match left. We'll play for pride and hope for a miracle. We needed a draw to keep our fate in our hands and couldn't get it."
