The 1958–59 season was Dinamo București's tenth season in Divizia A. Dinamo finishes second in the championship, one point behind the winners, Petrolul Ploiesti, but wins for the first time Cupa Romaniei. In this competition, Dinamo manages to pass by their main rivals, UTA, CCA, and Rapid. It is the first trophy for Iuliu Baratky as coach, after four Romanian Cups won as a player.