Ecuador had never beaten Mexico in the tournament but attacked from the kick-off and scored with one of the few clear chances of the first half.
Miler Bolanos broke from his own half and fed Enner Valencia on the left before a return pass left him with a simple tap-in from two metres.
The pair combined again for a second goal after 57 minutes. Bolanos stole possession near the halfway line and his neat through-ball allowed the West Ham United striker to score.
Mexico scored seven minutes later from the penalty spot, with Raul Jimenez making no mistake from the spot after defender Gabriel Achilier had climbed all over Hugo Ayala.
The result saw Ecuador leapfrog Mexico into third place in Group A behind Chile and Bolivia who have both already qualified and meet later on Friday.
The top two teams from each of the three groups qualify automatically along with the two best third-placed sides.
Ecuador have three points and a goal difference of -2 so must hope rivals in groups B and C lose heavily on the weekend.
Mexico, meanwhile, extended their shocking Copa America run to six games without a win.
They decided against sending a full-strength squad to the tournament, leaving big names such as Chicharito Hernandez and Carlos Vela for next month's Gold Cup in the United States.
(Writing by Andrew Downie, editing by Tony Jimenez)
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