One of the most extraordinary European players ever, he won hundreds of tournaments during the peak of his table tennis career (1964–1986), from Tokyo and Novi Sad to Beijing and Zagreb. His partner in doubles was the almost equally powerful player Antun Stipančić-Tova. Šurbek competed with Zoran Primorac at the 1992 Summer Olympics for Croatia when he was 46 years old.

Dragutin Šurbek's biggest successes were two World Championship titles in the Men's Doubles event. He won gold medals in 1979 (with Stipančić) and in 1983 (with Zoran Kalinić). In the Men's Singles event, he won the bronze medal three times (in 1971, 1973 and 1981). He was the European champion in Men's Singles in 1968 and in Men's Doubles in 1970, 1982 and 1984. With the SFR Yugoslavia national team, he was European champion in 1976.

He also won two English Open titles.

He received the Golden Badge award for the best athlete of Yugoslavia in 1983.

In later life, Šurbek was a table tennis coach in Zagreb.