Chicharito struck in the seventh minute at the Azteca with a deft chip over goalkeeper Keylor Navas to equal the Mexican record set by former striker Jared Borgetti in 2008.
Defender Nestor Araujo increased Mexico's lead on the stroke of halftime when he headed in a corner.
The victory lifted Mexico over Costa Rica into top place in the fifth and final phase of CONCACAF qualifying for the 2018 finals in Russia with seven points from three matches.
Costa Rica are second with six points and Panama third with four -- after their 1-0 defeat away to Trinidad and Tobago -- in the three automatic qualifying berths.
The team finishing in fourth place when the matches in the six-nation group are completed plays off over two legs against an Asian side for one more place at the finals.
(Reporting by Carlos Calvo; Writing by Rex Gowar in Buenos Aires; editing by Sudipto Ganguly)
