On the way to the final, Cerundolo beat first-seeded Casper Ruud and fifth-seeded Pablo Carreno Busta, among others.
Baez also did not have an easy way to the final.
He needed, among other things, to get past the former world ninth Fabio Fognini and second-seeded Andrej Rublev.
It was an even final, but in the end Cerundolo pulled the longer straw after 2-0 in the set.
In the first set, a tiebreak was required to separate the two Argentines.
The set numbers were written 7-6, 6–2.