Funes Mori capitalized on poor Mexico defense to head in uncontested from close range after receiving Paulo Dybala’s floating free-kick at the Mario Alberto Kempes stadium in the central Argentine city.
The hosts doubled their lead when Isaac Brizuela turned the ball into his own net seven minutes from the time.
The teams will meet again in Mendoza, western Argentina, on Tuesday.
Meanwhile, defender Kendall Watson scored twice in Costa Rica’s 3-2 away victory over Chile, also on Friday.
Ronald Matarrita was also on target for the visitors while Sebastian Vegas and Alexis Sanchez struck for the hosts at the Teniente Stadium in Rancagua, near Santiago.