The 20-year-old Rigondeux scored an 18-12 decision over Raimkoul Malakhbekov at 119 pounds Saturday (Friday night EDT).
"I'm very happy to have won," Rigondeaux said. "I thank my coach for teaching me how to do it. ... The other guy was very technical, but I beat him. I hope to fight again in the next Olympics."
Rigondeaux was just too quick for the Russian and took charge in the final two rounds after trailing 7-6 after the second round.
Mario Kindelan, a 29-year-old world champion, gave Cuba it's second gold by outboxing Andriy Kotelnyk of Ukraine 14-4 at 132 pounds.
Kotelnyk couldn't solve the left-handed Kindelan's defense. The Cuban also opened up in the final two rounds after leading only 3-2 after the second.
The other two Cuban finalists boxed later on the card.
The two American finalists will fight Sunday afternoon.
World 125-pound champion Rocky Juarez of Houston, will box Bekzat Sattarkhanov of Kazakstan, and Ricardo Williams Jr., of Cincinnati will box Mahamadkadyz Abdullaev, the 139-pound world champion from Uzbekistan.
The first gold medal of the games was won by Brahim Asloum of France, who won the 106-pound title on a 23-10 decision over 30-year-old Rafael Lozano, of Spain, a bronze medalist in 1996 appearing in his third Olympics.
Lozano had outpointed Asloum in a previous meeting, and when he learned he would be fighting the Spaniard for the gold medal, Asloum had said, "I have improved a lot and I am out to take revenge, and I always win my grudge match."
"It's my third time," said the 4-foot-11 Lozano, who could not get inside against the 5-5 Asloum and fell behind 17-7 after three rounds. "I tried. I will enjoy the silver medal."