Ungemach, Armin Weyrauch, Armin Eichholz, Bahne Rabe and Jorg Dederding won the 1991 World Championship in the coxed four in world record time (5:58,96), which is still unbeaten. He won another world title with the German eight in 1990 in Tasmania (Australia). Ungemach rowed in the final of the coxless four in 1992 Barcelona Spain and became fourth in a heartbeat final. Other highlights were the win of the Royal Henley Regatta, Good Will Games Seattle, Head of the Charles Boston and 12 German Championships in all boat classes.
With his pair partner Colin von Ettingshausen he represented Germany on various world titles and in the Atlanta Olympics 1996 in the coxless pair. Matthias Ungemach retired from professional rowing afterwards.
Ungemach lives with his family on the Northern Beaches in Sydney Australia and is married to Judith Ungemach (née: Judith Zeidler) who won Olympic Gold in the women's eight in Seoul (1988) and Bronze in Barcelona (1992).