The native of Cuba who emigrated to Miami, FL, Zamora was signed by the Astros from Cleveland but sold him to the Cubs where he made his debut in 1974 at age 29. He pitched for Chicago for three seasons and was eventually re-signed by Houston. He made ten appearances with the Astros in 1978 with no record but a 7.20 ERA to conclude his big league career. Overall, Zamora compiled a 13-14 record with 23 saves and a 4.53 ERA.