While Vízner had played tournaments in 1988 and 1989 before professionalism in 1990, he won his first title in Prague in 1993 on the Challenger circuit, defeating Swedes Tomas Nydahl and Mikael Tillström in the final, partnered by David Rikl, also a player with a higher doubles ranking and ultimately more success.

His next title he won with Paul Kilderry over Anders Järryd and number 7 doubles player Mark Knowles in a tournament in Rosmalen, Netherlands.

He made the finals of tournaments in these three years as well, and lost a close match at the 1999 Wimbledon Championships to 6th-ranked Olivier Delaître and 12th-ranked Fabrice Santoro in the second round of doubles competition along with Peter Tramacchi, in five sets, 4–6, 6–3, 3–6, 6–1, 3–6.

His equalled-best Grand Slam performance to date came in 2001 where he and Petr Pála lost in the final of the 2001 French Open to Indians Mahesh Bhupathi and Leander Paes.

The team defended their Costa do Sauípe title and continued their success to make the finals of Acapulco right after, but lost to Potito Starace and Martín Vassallo Argüello 0–6, 2–6.

He went on to equal his best Grand Slam performance by making the finals of the 2007 French Open men's doubles tournament with Lukáš Dlouhý, notching a win over co-ranked number ones and twin brothers Bob and Mike Bryan, and then beat 2006 Wimbledon runners-up Fabrice Santoro and Nenad Zimonjić.

En route, the team took out Leander Paes and Martin Damm, the defending U.S. Open champions of 2006 for men's doubles, and Bob and Mike Bryan in the semifinals.