The fighters could not be separated after a tight opening round, but Falcao tried to take the lead early in the second.
He caught La Cruz with a decent left hook as the Cuban stepped in looking to land with one of his own.
The Brazilian edged in front 10-9 after two rounds but La Cruz looked like he had another gear or two.
Indeed, the Cuban bombed forward in the final round looking to turn the contest around but found Falcao timing his punches excellently.
La Cruz pressed his opponent around the ring as the seconds ticked away. The Brazilian was hitting and moving nicely, but he could not shake La Cruz off.
The judges awarded Falcao a 18-15 victory.