In a match at BMO Stadium in Los Angeles, the striker scored in the 30th minute, converting a cross from Canadian midfielder Mathieu Choinière on the right with a left-footed finish into the net.
The goal was his second of the season, ending a drought after going scoreless in nine consecutive matches since his last goal in mid-February.
LAFC added two more goals from Venezuelan forward David Martínez who scored in the 39th and 58th minutes to secure the win and put the club in a favorable position to reach the semifinals.
Son was substituted by American Nathan Ordaz just minutes before injury time.
The LAFC's second leg match will be played in Puebla, Mexico next Tuesday.
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