Díaz made his Chilean Primera División début on 27 July 2009, in a 2–0 win over Deportes La Serena at San Carlos de Apoquindo. He scored his first two goals for the club on 23 August, both in a single match against Cobreloa, in where Católica won 2–0 thanks to the goals of Díaz. One month later, he scored his first hat-trick in his career in Católica's 7-0 thrashing of Curicó Unido, should be noted that one of his three goals was olympic. Díaz also scored in the following week against Audax Italiano, match that was won 4–0 by Católica. In that season, Damián was fully consolidated in the position of playmaker at the scheme of Católica's coach, Marco Antonio Figueroa. He was also paired in attack with Juan José Morales and Milovan Mirosevic. The team reached the final against Colo-Colo, but lost 6–4 on aggregate. Following his debut season in the Chilean Primera División, Díaz emerged as one of the league's finest playmakers.