Kick-off in Mexico City on Tuesday (Wednesday AEST) was delayed by an hour due to a thunderstorm, but that did not stop the hosts from making an electrifying start in front of more than 80,000 raucous fans.
Gilberto Mora fired narrowly over from distance and Raul Jimenez headed a fraction wide inside the first 10 minutes, while John Yeboah hit the post for Ecuador against the run of play before Mexico went ahead midway through the first half.
Julian Quinones was sent clear down the left by Roberto Alvarado and cut inside before firing into the top corner.
Another fine finish doubled Mexico's advantage in the 31st minute, Jimenez linking up with Quinones before smashing his shot into the roof of the net from the edge of the area.
Yeboah was denied by Raul Rangel before halftime as Ecuador sought a route back into the game.
Ecuador keeper Hernan Galindez made an excellent save after 66 minutes to keep out a Cesar Montes header from a corner, while at the other end Kevin Rodriguez prodded wide when played in by Moises Caicedo, but the South American side were unable to mount any sort of comeback.
A miserable evening for Ecuador was compounded by Arsenal defender Piero Hincapie being sent off in added time for covering his mouth during a verbal altercation with Santiago Gimenez.
Mexico had not won a knockout-stage match since defeating Bulgaria in the round of 16 when they hosted the tournament in 1986.
El Tricolor subsequently lost seven consecutive times at that same stage in 1994, 1998, 2002, 2006, 2010, 2014 and 2018.
In Qatar four years ago, they were eliminated in the group stage for the first time since Argentina '78.
With the AP.
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