In 1958, Ubriaco started his professional career with the New Westminster Royals and later played for Leafs' affiliates Rochester Americans and Pittsburgh Hornets. By 1962, Ubriaco wished to settle down with a team and start a family and asked for a trade from the Leafs. The Leafs accommodated his wish and he was traded to the Hershey Bears of the AHL. Ubriaco was very successful with the Bears, with a personal-best season of 38 goals and 86 points in the 1965–66 season. When the 1967 NHL Expansion came, and a potential chance to play in the NHL came, the Bears were not NHL-affiliated and this meant that Ubriaco was not eligible for the 1967 NHL Expansion Draft. Working for a broadcaster at the time, and covering the draft, Ubriaco learned that his only path to playing in the NHL was to hold out from the Bears. Ubriaco held out and was traded to the newly formed Pittsburgh Penguins. Ubriaco played parts of two seasons before being traded to the Oakland Seals. He was traded again, one season later, to the Chicago Black Hawks. He retired after the 1969–70 season after having played 177 NHL games. Ubriaco recorded 39 goals and 35 assists for 74 career points.