The major highlights of Hlasek's career came in 1992. He won the French Open men's doubles title that year (partnering fellow Swiss player Marc Rosset). He was also a member of Switzerland Davis Cup team which reached the final of the 1992 Davis Cup (where they were defeated by the United States), and won the 1992 Hopman Cup (partnering Manuela Maleeva-Fragnière). His best Grand Slam performance was reaching the quarter finals of the 1991 French Open, defeating David Pate, Emilio Sánchez, Tomás Carbonell and Christian Miniussi before losing to Andre Agassi.